diff --git a/lib/OrdinaryDiffEqDifferentiation/src/OrdinaryDiffEqDifferentiation.jl b/lib/OrdinaryDiffEqDifferentiation/src/OrdinaryDiffEqDifferentiation.jl
index 8bb0cbe90f9..bca939c332e 100644
--- a/lib/OrdinaryDiffEqDifferentiation/src/OrdinaryDiffEqDifferentiation.jl
+++ b/lib/OrdinaryDiffEqDifferentiation/src/OrdinaryDiffEqDifferentiation.jl
@@ -36,6 +36,7 @@ using OrdinaryDiffEqCore: OrdinaryDiffEqAlgorithm, OrdinaryDiffEqAdaptiveImplici
     OrdinaryDiffEqImplicitAlgorithm, CompositeAlgorithm,
     OrdinaryDiffEqExponentialAlgorithm,
     OrdinaryDiffEqAdaptiveExponentialAlgorithm,
+    OrdinaryDiffEqLinearExponentialAlgorithm,
     StochasticDiffEqNewtonAlgorithm, StochasticDiffEqNewtonAdaptiveAlgorithm,
     StochasticDiffEqJumpNewtonAdaptiveAlgorithm,
     StochasticDiffEqJumpNewtonDiffusionAdaptiveAlgorithm,
diff --git a/lib/OrdinaryDiffEqDifferentiation/src/alg_utils.jl b/lib/OrdinaryDiffEqDifferentiation/src/alg_utils.jl
index 75b724ab495..073e88b4c5c 100644
--- a/lib/OrdinaryDiffEqDifferentiation/src/alg_utils.jl
+++ b/lib/OrdinaryDiffEqDifferentiation/src/alg_utils.jl
@@ -32,6 +32,12 @@ function _alg_autodiff(
     ) where {CS, AD, FDT, ST, CJ, Controller}
     return Val{AD}()
 end
+# OrdinaryDiffEqLinearExponentialAlgorithm subtypes (Magnus integrators, LieEuler,
+# CG methods, etc.) have NO autodiff field — their only fields are krylov, m, iop.
+# They must be excluded before the generic ExponentialAlgorithm dispatch below.
+function _alg_autodiff(::OrdinaryDiffEqLinearExponentialAlgorithm)
+    return Val{false}()
+end
 function _alg_autodiff(
         alg::Union{
             OrdinaryDiffEqExponentialAlgorithm{CS, AD},
diff --git a/lib/OrdinaryDiffEqDifferentiation/test/differentiation_traits_tests.jl b/lib/OrdinaryDiffEqDifferentiation/test/differentiation_traits_tests.jl
index b00c3c8e3bb..c5a9b72d714 100644
--- a/lib/OrdinaryDiffEqDifferentiation/test/differentiation_traits_tests.jl
+++ b/lib/OrdinaryDiffEqDifferentiation/test/differentiation_traits_tests.jl
@@ -43,3 +43,26 @@ sol = solve(prob2, Rosenbrock23(autodiff = AutoForwardDiff(chunksize = 1)))
 
 sol = solve(prob2, Rosenbrock23(autodiff = AutoFiniteDiff()))
 @test ≈(good_sol[:, end], sol[:, end], rtol = 1.0e-2)
+
+# Regression test for issue #3232:
+# MagnusGL6 (and all OrdinaryDiffEqLinearExponentialAlgorithm subtypes)
+# have no `autodiff` field. When OrdinaryDiffEqDifferentiation is loaded,
+# _alg_autodiff must not crash by trying to access alg.autodiff.
+using OrdinaryDiffEqLinear
+using SciMLOperators: MatrixOperator
+
+@testset "MagnusGL6 solve with Differentiation loaded (issue #3232)" begin
+    function update_func!(A, u, p, t)
+        A[1, 1] = cos(t)
+        A[2, 1] = sin(t)
+        A[1, 2] = -sin(t)
+        A[2, 2] = cos(t)
+    end
+    A = MatrixOperator(ones(2, 2), update_func! = update_func!)
+    prob = ODEProblem(A, ones(2), (1.0, 6.0))
+
+    # This would crash with FieldError before the fix
+    sol = solve(prob, MagnusGL6(), dt = 1 / 10)
+    @test sol.retcode == ReturnCode.Success
+    @test length(sol.t) > 1
+end
diff --git a/lib/OrdinaryDiffEqLinear/test/linear_method_tests.jl b/lib/OrdinaryDiffEqLinear/test/linear_method_tests.jl
index b49d19b0c1e..c5a62556ce9 100644
--- a/lib/OrdinaryDiffEqLinear/test/linear_method_tests.jl
+++ b/lib/OrdinaryDiffEqLinear/test/linear_method_tests.jl
@@ -267,3 +267,21 @@ test_setup = Dict(:alg => Vern9(), :reltol => 1.0e-14, :abstol => 1.0e-14)
 
 sim = analyticless_test_convergence(dts, prob, CayleyEuler(), test_setup)
 @test sim.𝒪est[:l2] ≈ 1 atol = 0.2
+
+# Regression test for https://github.com/SciML/OrdinaryDiffEq.jl/issues/3232
+# Magnus/Linear integrators must not FieldError when OrdinaryDiffEqDifferentiation
+# is loaded (which happens transitively via DifferentialEquations.jl).
+@testset "Regression #3232: non-autonomous Magnus solve does not FieldError" begin
+    function update_func_3232!(A, u, p, t)
+        A[1, 1] = cos(t)
+        A[2, 1] = sin(t)
+        A[1, 2] = -sin(t)
+        A[2, 2] = cos(t)
+    end
+    A_3232 = MatrixOperator(ones(2, 2), update_func! = update_func_3232!)
+    prob_3232 = ODEProblem(A_3232, ones(2), (1.0, 6.0))
+    for alg in (MagnusGL6(), MagnusGL4(), MagnusGL8(), LieEuler(), CG2(), CG3(), CG4a())
+        sol = solve(prob_3232, alg, dt = 1 / 10)
+        @test sol.retcode == ReturnCode.Success
+    end
+end