diff --git a/tests/unit/test_integrators.py b/tests/unit/test_integrators.py
new file mode 100644
index 00000000..81a84266
--- /dev/null
+++ b/tests/unit/test_integrators.py
@@ -0,0 +1,41 @@
+"""Unit tests for simulation integrators."""
+
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pytest
+
+from crazyflow.sim import Sim
+from crazyflow.sim.integration import Integrator
+
+
+@pytest.mark.unit
+@pytest.mark.parametrize("integrator", Integrator)
+def test_sim_step_integrators(integrator: Integrator, device: str):
+    """Every integrator stays close to the default after two simulation steps."""
+    sim = Sim(integrator=integrator, device=device)
+    default_sim = Sim(device=device)
+    sim.step(2)
+    default_sim.step(2)
+
+    data, structure = jax.tree.flatten_with_path(sim.data)
+    default_data, default_structure = jax.tree.flatten(default_sim.data)
+    assert structure == default_structure, "Simulation data structures must match"
+    for (path, value), default_value in zip(data, default_data, strict=True):
+        name = jax.tree_util.keystr(path)
+        if isinstance(value, jnp.ndarray):
+            if jax.dtypes.issubdtype(value.dtype, jax.dtypes.prng_key):
+                np.testing.assert_array_equal(
+                    jax.random.key_data(value), jax.random.key_data(default_value), err_msg=name
+                )
+            elif jnp.issubdtype(value.dtype, jnp.inexact):
+                # Rotor speeds differ by several percent between Euler and RK4.
+                np.testing.assert_allclose(
+                    value, default_value, rtol=2e-2, atol=1e-4, err_msg=name, strict=True
+                )
+            else:
+                np.testing.assert_array_equal(value, default_value, err_msg=name, strict=True)
+        else:
+            assert value == default_value, f"{name}: Value mismatch"
+    sim.close()
+    default_sim.close()