diff --git a/.github/workflows/cache-perf.yml b/.github/workflows/cache-perf.yml
new file mode 100644
index 0000000..2a1d78a
--- /dev/null
+++ b/.github/workflows/cache-perf.yml
@@ -0,0 +1,48 @@
+name: Cache performance testing
+
+# Only run manually: the purpose of this test is to check how much (if at all)
+# using the caches helps, and that's not something that needs doing often, and
+# it is something that's time consuming.
+on: workflow_dispatch
+
+# Avoid running at the same time as other actions that interfere with caches,
+# to avoid pollution.
+concurrency: caches
+
+jobs:
+  clear-caches:
+    uses: ./.github/workflows/clear-caches.yml
+    permissions:
+      actions: write
+
+  # There should now be no cache, so we can test how long it takes to do an
+  # install without a cache while building the cache for the later action.
+  install-without-cache:
+    runs-on: windows-latest
+    needs: clear-caches
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: Install a large set of Cygwin packages
+        uses: ./
+        with:
+          packages: >
+            biber doxygen evolution kde-dev-utils
+            mkvtoolnix-debuginfo nghttp x11vnc
+          package-cache: saveonly
+
+  install-with-cache:
+    runs-on: windows-latest
+    needs: install-without-cache
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: Install a large set of Cygwin packages
+        uses: ./
+        with:
+          packages: >
+            biber doxygen evolution kde-dev-utils
+            mkvtoolnix-debuginfo nghttp x11vnc
+          package-cache: enabled
diff --git a/.github/workflows/cache-test.yml b/.github/workflows/cache-test.yml
new file mode 100644
index 0000000..212d046
--- /dev/null
+++ b/.github/workflows/cache-test.yml
@@ -0,0 +1,173 @@
+name: Caching tests
+
+on: [push, pull_request]
+
+# Ensure there's only a single version of this running in any repo, so one set
+# of tests won't create or destroy caches that interfere with another run.
+concurrency: caches
+
+jobs:
+  clear-caches:
+    uses: ./.github/workflows/clear-caches.yml
+    permissions:
+      actions: write
+
+  test-caching:
+    runs-on: windows-latest
+
+    needs: clear-caches
+
+    # Ordering is important here to ensure the correct things are in the
+    # correct caches at the correct times.
+    #
+    # This also relies on having six Cygwin packages that don't have any
+    # cross-dependencies (and ideally are small and have few dependencies of
+    # their own), so we can distinguish what's cached at what step.
+    #
+    # We test for the correct behaviour in the following circumstances:
+    #
+    # option      | saves   | restores
+    # ------------+---------+----------
+    # disabled    | no (1)  | no (5)
+    # enabled     | yes (2) | yes (6)
+    # saveonly    | yes (3) | no (7)
+    # restoreonly | no (4)  | yes (8)
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: Install Cygwin + bash_completion, no caching
+        uses: ./
+        with:
+          packages: bash-completion
+          package-cache: disabled
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin + brotli, with caching
+        uses: ./
+        with:
+          packages: brotli
+          package-cache: enabled
+
+      # This assumes 6 and tests 1
+      - name: Ensure bash-completion not downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/bash-completion-*.tar.*; do
+            [[ -f "$file" ]] && exit 1
+          done
+          exit 0
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin + libyajl2, with caching
+        uses: ./
+        with:
+          packages: libyajl2
+          package-cache: enabled
+
+      # This tests 2 and 6
+      - name: Ensure brotli downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/brotli-*.tar.*; do
+            [[ -f "$file" ]] && exit 0
+          done
+          exit 1
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin + mksh, saveonly
+        uses: ./
+        with:
+          packages: mksh
+          package-cache: saveonly
+
+      # This assumes 2 and tests 7
+      - name: Ensure libyajl2 not downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/libyajl2-*.tar.*; do
+            [[ -f "$file" ]] && exit 1
+          done
+          exit 0
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin + libgif7, restoreonly
+        uses: ./
+        with:
+          packages: libgif7
+          package-cache: restoreonly
+
+      # This tests 3 and 8
+      - name: Ensure mksh downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/mksh-*.tar.*; do
+            [[ -f "$file" ]] && exit 1
+          done
+          exit 0
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin, restoreonly
+        uses: ./
+        with:
+          package-cache: restoreonly
+
+      # This assumes 8 and tests 4
+      - name: Ensure libgif7 not downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/libgif7-*.tar.*; do
+            [[ -f "$file" ]] && exit 1
+          done
+          exit 0
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
+
+      - name: Install Cygwin, caching disabled
+        uses: ./
+        with:
+          package-cache: disabled
+
+      # This assumes 3 and tests 5
+      - name: Ensure mksh not downloaded
+        shell: C:\cygwin\bin\bash.exe --noprofile --norc -e -o pipefail -o igncr {0}
+        run: |
+          for file in /cygdrive/c/cygwin-packages/*/*/*/*/mksh-*.tar.*; do
+            [[ -f "$file" ]] && exit 1
+          done
+          exit 0
+
+      - name: Delete the Cygwin installation and downloaded packages
+        run: |
+          Remove-Item -Force -Recurse C:\cygwin
+          Remove-Item -Force -Recurse C:\cygwin-packages
+          Remove-Item -Force -Recurse C:\cygwin-packages-checksum.*
diff --git a/.github/workflows/clear-caches.yml b/.github/workflows/clear-caches.yml
new file mode 100644
index 0000000..12c2d24
--- /dev/null
+++ b/.github/workflows/clear-caches.yml
@@ -0,0 +1,29 @@
+name: Clear Cygwin package caches
+
+on: workflow_call
+
+jobs:
+  clear-caches:
+    runs-on: ubuntu-latest
+    permissions:
+      actions: write
+    steps:
+      # This will only delete up to 100 caches.  That should be far more than
+      # is ever needed.
+      - name: Delete cache entries
+        uses: actions/github-script@v6
+        with:
+          script: |
+            const response = await github.rest.actions.getActionsCacheList({
+              owner: context.repo.owner,
+              repo: context.repo.repo,
+              per_page: 100,
+              key: 'cygwin-install-action-packages-'
+            });
+            for (const cache of response.data.actions_caches) {
+              await github.rest.actions.deleteActionsCacheById({
+                owner: context.repo.owner,
+                repo: context.repo.repo,
+                cache_id: cache.id
+              });
+            }
diff --git a/README.md b/README.md
index 54b1b66..138623c 100644
--- a/README.md
+++ b/README.md
@@ -18,14 +18,15 @@ Please fix my terrible cargo-cult PowerShell.
 Parameters
 ----------
 
-| Input       | Default                                      | Description
-| ----------- | -------------------------------------------- | -----------
-| platform    | x86_64                                       | Install the x86 or x86\_64 version of Cygwin.
-| packages    | *none*                                       | List of additional packages to install.
-| install-dir | C:\cygwin                                    | Installation directory
-| site        | http://mirrors.kernel.org/sourceware/cygwin/ | Mirror site to install from
-| check-sig   | true                                         | Whether to check the setup.ini signature
-| add-to-path | true                                         | Whether to add Cygwin's `/bin` directory to the system `PATH`
+| Input         | Default                                      | Description
+| ------------- | -------------------------------------------- | -----------
+| platform      | x86_64                                       | Install the x86 or x86\_64 version of Cygwin.
+| packages      | *none*                                       | List of additional packages to install.
+| install-dir   | C:\cygwin                                    | Installation directory
+| site          | http://mirrors.kernel.org/sourceware/cygwin/ | Mirror site to install from
+| check-sig     | true                                         | Whether to check the setup.ini signature
+| add-to-path   | true                                         | Whether to add Cygwin's `/bin` directory to the system `PATH`
+| package-cache | disabled                                     | Whether to cache the package downloads
 
 Line endings
 ------------
@@ -85,6 +86,40 @@ those executables directly in a `run:` in your workflow. Execute them via
 Alternatively, putting e.g. `CYGWIN=winsymlinks:native` into the workflow's
 environment works, since setup now honours that.
 
+Caching
+-------
+
+If you're likely to do regular builds, you might want to store the packages
+locally rather than needing to download them from the Cygwin mirrors on every
+build.  Set `package-cache` to `enabled` and the action will use [GitHub's
+dependency caching][0] to store downloaded package files between runs.
+
+[0]: https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows
+
+This has the effect of speeding up the run of the installation itself, at the
+expense of taking slightly longer before and after the installation to check
+and potentially update the cache.  The installer will still check for updated
+packages, and will download new packages if the cached ones are out of date
+
+In certain circumstances you might want to ignore any existing caches but still
+store a new one, or restore a cache but not write one.  Do this by setting
+`package-cache` to `saveonly` or `restoreonly` as appropriate.  This is
+particularly useful when calling the action multiple times in the same run,
+where you probably want to restore the cache the first time the action is
+called, then save it the last time it is called.
+
+You should make sure to clear these caches every so often.  This action, like
+the underlying Cygwin installer, doesn't remove old package files from its
+download directory, so if you don't clear the caches occasionally (and you run
+builds often enough that GitHub doesn't do it for you automatically) you'll
+find the caches keep getting larger as they gain more and more outdated and
+unused packages.  Either [delete them manually][1], [use a separate action or
+API call][2], or do occasional runs with `saveonly` to create a fresher small
+cache.
+
+[1]: https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows#deleting-cache-entries
+[2]: https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows#deleting-cache-entries
+
 Mirrors and signatures
 ----------------------
 
diff --git a/action.yml b/action.yml
index a6b6b95..31bab52 100644
--- a/action.yml
+++ b/action.yml
@@ -26,10 +26,35 @@ inputs:
     description: Should Cygwin's bin directory be added to the system PATH?
     required: false
     default: true
+  package-cache:
+    description: Cache package downloads for speed
+    required: false
+    default: disabled
 
 runs:
   using: "composite"
   steps:
+    - uses: actions/cache/restore@v3
+      if: inputs.package-cache-behaviour == 'enabled' || inputs.package-cache-behaviour == 'restoreonly'
+      with:
+        key: cygwin-install-action-packages-${{ github.run_id }}-${{ github.run_attempt }}-${{ github.job }}-${{ github.action }}
+        path: C:\cygwin-packages
+        restore-keys:
+          cygwin-install-action-packages-${{ github.run_id }}-${{ github.job }}-${{ github.run_attempt }}-
+          cygwin-install-action-packages-${{ github.run_id }}-${{ github.job }}-
+          cygwin-install-action-packages-${{ github.run_id }}-
+          cygwin-install-action-packages-
+
+    - if: inputs.package-cache-behaviour == 'enabled' || inputs.package-cache-behaviour == 'restoreonly'
+      working-directory: C:\
+      shell: bash
+      run: |
+        if [[ -d cygwin-packages ]]; then
+          find cygwin-packages -type f ! -name setup.ini -print0 |
+            sort -z |
+            xargs -0 b2sum >cygwin-packages-checksum.old
+        fi
+
     - run: |
         $platform = '${{ inputs.platform }}'
         $platform = $platform -replace '^(x64|amd64)$', 'x86_64'
@@ -82,6 +107,26 @@ runs:
         & C:\setup.exe $args | Out-Default
       shell: powershell
 
+    - if: inputs.package-cache-behaviour == 'enabled' || inputs.package-cache-behaviour == 'saveonly'
+      id: refresh-cache
+      working-directory: C:\
+      shell: bash
+      run: |
+        if [[ -d cygwin-packages ]]; then
+          find cygwin-packages -type f ! -name setup.ini -print0 |
+            sort -z |
+            xargs -0 b2sum >cygwin-packages-checksum.new
+          if ! diff cygwin-packages-checksum.old cygwin-packages-checksum.new; then
+            printf 'update_package_cache=YesPlease\n' >>"$GITHUB_OUTPUT"
+          fi
+        fi
+
+    - if: steps.refresh-cache.outputs.update_package_cache != ''
+      uses: actions/cache/save@v3
+      with:
+        key: cygwin-install-action-packages-${{ github.run_id }}-${{ github.run_attempt }}-${{ github.job }}-${{ github.action }}
+        path: C:\cygwin-packages
+
     - if: ${{ inputs.add-to-path  == 'true' }}
       run: echo "${{ inputs.install-dir }}\bin" >> $env:GITHUB_PATH
       shell: powershell