diff --git a/test/alloc_tests.jl b/test/alloc_tests.jl
new file mode 100644
index 0000000..1a5cb33
--- /dev/null
+++ b/test/alloc_tests.jl
@@ -0,0 +1,92 @@
+using SimpleDiffEq
+using DiffEqBase
+using StaticArrays
+using Test
+
+@testset "Allocation Tests - Zero Allocation Verification" begin
+    # Define test problems (Lorenz system)
+    function loop_oop(u, p, t)
+        @inbounds begin
+            σ = p[1]
+            ρ = p[2]
+            β = p[3]
+            du1 = σ * (u[2] - u[1])
+            du2 = u[1] * (ρ - u[3]) - u[2]
+            du3 = u[1] * u[2] - β * u[3]
+            return SVector{3}(du1, du2, du3)
+        end
+    end
+
+    function loop_iip!(du, u, p, t)
+        σ = p[1]
+        ρ = p[2]
+        β = p[3]
+        du[1] = σ * (u[2] - u[1])
+        du[2] = u[1] * (ρ - u[3]) - u[2]
+        du[3] = u[1] * u[2] - β * u[3]
+        return nothing
+    end
+
+    u0_vec = [10.0, 10.0, 10.0]
+    u0_svec = SVector{3}(10.0, 10.0, 10.0)
+    dt = 0.01
+    p = [10.0, 28.0, 8 / 3]
+
+    @testset "SimpleTsit5 step! - zero allocations" begin
+        # OOP (out-of-place) with SVector
+        integ_oop = SimpleDiffEq.simpletsit5_init(loop_oop, false, u0_svec, 0.0, dt, p)
+        step!(integ_oop)  # warmup
+        allocs = @allocated step!(integ_oop)
+        @test allocs == 0
+
+        # IIP (in-place) with Vector
+        integ_iip = SimpleDiffEq.simpletsit5_init(loop_iip!, true, copy(u0_vec), 0.0, dt, p)
+        step!(integ_iip)  # warmup
+        allocs = @allocated step!(integ_iip)
+        @test allocs == 0
+    end
+
+    @testset "SimpleRK4 step! - zero allocations" begin
+        # OOP (out-of-place) with SVector
+        integ_oop = SimpleDiffEq.simplerk4_init(loop_oop, false, u0_svec, 0.0, dt, p)
+        step!(integ_oop)  # warmup
+        allocs = @allocated step!(integ_oop)
+        @test allocs == 0
+
+        # IIP (in-place) with Vector
+        integ_iip = SimpleDiffEq.simplerk4_init(loop_iip!, true, copy(u0_vec), 0.0, dt, p)
+        step!(integ_iip)  # warmup
+        allocs = @allocated step!(integ_iip)
+        @test allocs == 0
+    end
+
+    @testset "SimpleEuler step! - zero allocations" begin
+        # OOP (out-of-place) with SVector
+        integ_oop = SimpleDiffEq.simpleeuler_init(loop_oop, false, u0_svec, 0.0, dt, p)
+        step!(integ_oop)  # warmup
+        allocs = @allocated step!(integ_oop)
+        @test allocs == 0
+
+        # IIP (in-place) with Vector
+        integ_iip = SimpleDiffEq.simpleeuler_init(loop_iip!, true, copy(u0_vec), 0.0, dt, p)
+        step!(integ_iip)  # warmup
+        allocs = @allocated step!(integ_iip)
+        @test allocs == 0
+    end
+
+    @testset "SimpleATsit5 step! - zero allocations" begin
+        # OOP (out-of-place) with SVector
+        prob_oop = ODEProblem{false}(loop_oop, u0_svec, (0.0, 100.0), p)
+        integ_oop = DiffEqBase.__init(prob_oop, SimpleATsit5(), dt = dt)
+        step!(integ_oop)  # warmup
+        allocs = @allocated step!(integ_oop)
+        @test allocs == 0
+
+        # IIP (in-place) with Vector
+        prob_iip = ODEProblem{true}(loop_iip!, copy(u0_vec), (0.0, 100.0), p)
+        integ_iip = DiffEqBase.__init(prob_iip, SimpleATsit5(), dt = dt)
+        step!(integ_iip)  # warmup
+        allocs = @allocated step!(integ_iip)
+        @test allocs == 0
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index ffd59d1..f562f3c 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -20,5 +20,6 @@ const GROUP = get(ENV, "GROUP", "Core")
         import Pkg
         Pkg.add("JET")
         @time @safetestset "JET Static Analysis Tests" include("jet_tests.jl")
+        @time @safetestset "Allocation Tests" include("alloc_tests.jl")
     end
 end