diff --git a/test/problems/goddard2.jl b/test/problems/goddard2.jl
new file mode 100644
index 00000000..536455b1
--- /dev/null
+++ b/test/problems/goddard2.jl
@@ -0,0 +1,42 @@
+# Goddard2 problem (version for :exa)
+# free final time, fixed final mass, max altitude
+# constraint on max speed
+
+function goddard2(; vmax=0.1, Tmax=3.5)
+    # constants
+    Cd = 310
+    β = 500
+    b = 2
+    r0 = 1
+    v0 = 0
+    m0 = 1
+    mf = 0.6
+    x0 = [r0, v0, m0]
+
+    goddard2 = @def begin
+        tf ∈ R, variable
+        t ∈ [0, tf], time
+        x = (r, v, m) ∈ R^3, state
+        u ∈ R, control
+        tf ≥ 0.01
+        x(0) == x0
+        m(tf) == mf
+        r0 ≤ r(t) ≤ r0 + 0.1
+        v0 ≤ v(t) ≤ vmax
+        mf ≤ m(t) ≤ m0
+        0 ≤ u(t) ≤ 1
+
+        ∂(r)(t) == v(t)
+        ∂(v)(t) == -Cd * v(t)^2 * exp(-β * (r(t) - 1)) / m(t) - 1 / r(t)^2 + u(t) * Tmax / m(t)
+        ∂(m)(t) == -b * Tmax * u(t)
+
+        r(tf) → max
+    end
+
+    return ((
+        ocp=goddard2,
+        obj=1.01257,
+        name="goddard2",
+        init=(state=[1.01, 0.05, 0.8],),
+    ))
+end
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diff --git a/test/runtests.jl b/test/runtests.jl
index 1f9e6584..cc996949 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -30,10 +30,11 @@ macro ignore(e) :() end
 # run either usual test suite on CPU, or GPU tests only 
 @testset verbose = true showtiming = true "Test CTDirect" begin
     if "GPU" in ARGS
-        # GPU tests only (moonshot workflow)
-        include("test_gpu.jl")
+        # ExaModels tests only on CPU + GPU (moonshot workflow)
+        include("test_exa.jl")
     else
         # CPU: run all scripts in subfolder suite/
         include.(filter(contains(r".jl$"), readdir("./suite"; join=true)))
+        include("test_exa.jl") # will only run CPU tests if GPU is not available
     end
 end
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diff --git a/test/test_exa.jl b/test/test_exa.jl
new file mode 100644
index 00000000..70129822
--- /dev/null
+++ b/test/test_exa.jl
@@ -0,0 +1,71 @@
+# ExaModels tests, CPU + GPU (when available)
+import ExaModels
+using MadNLP
+using MadNLPGPU
+using CUDA
+
+# beam2
+
+if !isdefined(Main, :beam2)
+    include("./problems/beam2.jl")
+end
+
+if !isdefined(Main, :goddard2)
+    include("./problems/goddard2.jl")
+end
+
+# test_exa for all backends (CPU + GPU)
+
+function test_exa(exa_backend)
+
+    # beam2
+
+    @testset verbose = true showtiming = true "beam2 :examodel :euler" begin
+        prob = beam2()
+        sol = solve(prob.ocp, :madnlp, :exa; disc_method = :euler, exa_backend = exa_backend, display = display)
+        @test sol.objective ≈ prob.obj rtol = 1e-2
+    end
+
+    @testset verbose = true showtiming = true "beam2 :examodel :trapeze" begin
+        prob = beam2()
+        sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, exa_backend = exa_backend, display = display)
+        @test sol.objective ≈ prob.obj rtol = 1e-2
+    end
+
+    @testset verbose = true showtiming = true "beam2 :examodel :trapeze :grid_size" begin
+        prob = beam2()
+        sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, exa_backend = exa_backend, display = display, grid_size = 1000)
+        @test sol.objective ≈ prob.obj rtol = 1e-2
+    end
+
+    @testset verbose = true showtiming = true "beam2 :examodel :trapeze :init" begin
+        prob = beam2()
+        sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, exa_backend = exa_backend, display = display, init=(control=6.66,), max_iter = 0)
+        @test control(sol)(0.5) == 6.66
+    end
+
+    # goddard2
+
+    @testset verbose = true showtiming = true "goddard2 :examodel :trapeze :grid_size" begin
+        prob = goddard2()
+        sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, exa_backend = exa_backend, display = display, grid_size = 1000)
+        @test sol.objective ≈ prob.obj rtol = 1e-2
+    end
+    
+end
+
+# CPU tests
+
+display = true
+println("testing: CPU with ExaModels + MadNLP")
+test_exa(nothing) # CPU tests
+
+# GPU tests
+
+display = true
+if CUDA.functional()
+    println("testing: GPU with ExaModels + MadNLPGPU + CUDA")
+    test_exa(CUDABackend()) # GPU tests
+else
+    println("********** CUDA is not available")
+end
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diff --git a/test/test_gpu.jl b/test/test_gpu.jl
deleted file mode 100644
index feef8bb4..00000000
--- a/test/test_gpu.jl
+++ /dev/null
@@ -1,49 +0,0 @@
-# GPU tests
-import ExaModels
-using MadNLPGPU
-using CUDA
-
-# beam2
-if !isdefined(Main, :beam2)
-    include("./problems/beam2.jl")
-end
-
-println("testing: GPU with ExaModels / MadNLPGPU / CUDA")
-display = true
-
-if CUDA.functional()
-    println("********** CUDA is available")
-    exa_backend = CUDA.functional() ? CUDABackend() : nothing
-else
-    error("********** CUDA is not available")
-    exa_backend = nothing 
-end
- 
-if !isnothing(exa_backend)
-println("GPU tests with ", exa_backend)
-@testset verbose = true showtiming = true ":examodel :GPU :euler" begin
-    prob = beam2()
-    sol = solve(prob.ocp, :madnlp, :exa; disc_method = :euler, exa_backend = exa_backend, display = display)
-    @test sol.objective ≈ prob.obj rtol = 1e-2
-end
-@testset verbose = true showtiming = true ":examodel :GPU :trapeze :init" begin
-    prob = beam2()
-    sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, exa_backend = exa_backend, display = display, init=(control=6.66,), max_iter = 0)
-    @test control(sol)(0.5) == 6.66
-end
-else
-    println("skipping GPU tests")
-end
-
-@ignore begin # debug
-# swimmer2
-if !isdefined(Main, :swimmer2)
-    include("../problems/swimmer2.jl")
-end
-
-@testset verbose = true showtiming = true ":examodel :cpu :swimmer2" begin
-    prob = swimmer2()
-    sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, display = display)
-    @test sol.objective ≈ prob.obj rtol = 1e-2
-end
-end # debug
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