diff --git a/lib/cufft/fft.jl b/lib/cufft/fft.jl
index c431453d1f..1bbe5ec688 100644
--- a/lib/cufft/fft.jl
+++ b/lib/cufft/fft.jl
@@ -455,3 +455,12 @@ function Base.:(*)(p::cCuFFTPlan{T,K,false,N}, x::DenseCuArray{T,M}) where {T,K,
     unsafe_execute_trailing!(p,x, y)
     y
 end
+
+## support adjoints of FFT plans
+
+AbstractFFTs.AdjointStyle(::cCuFFTPlan) = AbstractFFTs.FFTAdjointStyle()
+AbstractFFTs.AdjointStyle(::rCuFFTPlan{T, CUFFT_FORWARD}) where {T} = AbstractFFTs.RFFTAdjointStyle()
+AbstractFFTs.AdjointStyle(p::rCuFFTPlan{T, CUFFT_INVERSE}) where {T} = AbstractFFTs.IRFFTAdjointStyle(p.osz[first(p.region)])
+
+# manually resolve ambiguity in adjoint plan application
+Base.:(*)(p::AbstractFFTs.AdjointPlan{T}, x::CuArray) where T = Base.invoke(*, Tuple{AbstractFFTs.AdjointPlan, AbstractArray}, p, x)
\ No newline at end of file
diff --git a/test/libraries/cufft.jl b/test/libraries/cufft.jl
index 6c3cbfa200..e45c2ab6ce 100644
--- a/test/libraries/cufft.jl
+++ b/test/libraries/cufft.jl
@@ -342,3 +342,10 @@ end
 
     @test Array(dy) ≈ y
 end
+
+## AbstractFFTs tests, which also test adjoint functionality of CUFFT plans. 
+
+@testset "AbstractFFTs FFT backend tests" begin
+    AbstractFFTs.TestUtils.test_complex_ffts(CuArray; test_wrappers=false)
+    AbstractFFTs.TestUtils.test_real_ffts(CuArray; copy_input=true, test_wrappers=false)
+end