diff --git a/equinox/_ad.py b/equinox/_ad.py
index f2f1db8f..3b9a2825 100644
--- a/equinox/_ad.py
+++ b/equinox/_ad.py
@@ -344,12 +344,13 @@ def _fn(*_flat_dynamic):
         _in = combine(_dynamic, static_primals)
         _out = fn(*_in, **kwargs)
         _dynamic_out, _static_out = partition(_out, _is_jvp_tracer(_main))
-        return _dynamic_out, Static(_static_out)
+        _arr_out, _non_arr_out = partition(_static_out, is_array)
+        return _dynamic_out, _arr_out, Static(_non_arr_out)
 
     primal_out, tangent_out = jax.jvp(_fn, flat_dynamic_primals, flat_tangents)
-    dynamic_primal_out, static_primal_out = primal_out
-    primal_out = combine(dynamic_primal_out, static_primal_out.value)
-    tangent_out, _ = tangent_out
+    dynamic_primal_out, arr_primal_out, static_primal_out = primal_out
+    primal_out = combine(dynamic_primal_out, arr_primal_out, static_primal_out.value)
+    tangent_out, _, _ = tangent_out
 
     return primal_out, tangent_out
 
diff --git a/equinox/_module.py b/equinox/_module.py
index 7e0fe5f0..de5b7f1f 100644
--- a/equinox/_module.py
+++ b/equinox/_module.py
@@ -24,7 +24,7 @@
 from ._better_abstract import ABCMeta, dataclass
 from ._caches import cache_clears
 from ._doc_utils import doc_repr
-from ._filters import is_array_like
+from ._filters import is_array, is_array_like
 from ._pretty_print import tree_pformat
 from ._tree import tree_equal
 
@@ -584,6 +584,19 @@ def __call__(cls, *args, **kwargs):
                 f"The following fields were not initialised during __init__: "
                 f"{missing_names}"
             )
+        # [Step 3.5] Prevent arrays from being marked as static
+        for field in dataclasses.fields(self):
+            if field.metadata.get("static", False):
+                if any(
+                    jtu.tree_map(
+                        is_array, jtu.tree_flatten(getattr(self, field.name))[0]
+                    )
+                ):
+                    warnings.warn(
+                        "A JAX array is being set as static! This can result "
+                        "in unexpected behavior and is usually a mistake to do.",
+                        stacklevel=2,
+                    )
         # Freeze.
         object.__setattr__(self, "__class__", cls)
         # [Step 4] Run any custom validators. (After freezing; as they run
diff --git a/equinox/_vmap_pmap.py b/equinox/_vmap_pmap.py
index 216619f7..6da7b0cc 100644
--- a/equinox/_vmap_pmap.py
+++ b/equinox/_vmap_pmap.py
@@ -206,25 +206,28 @@ def _fun_wrapper(_dynamic_args):
             _out_axes = _resolve_axes(_out, _out_axes)
             _none_axes = jtu.tree_map(_is_none, _out_axes, is_leaf=_is_none)
             _nonvmapd, _vmapd = partition(_out, _none_axes, is_leaf=_is_none)
-            return _vmapd, Static((_nonvmapd, _out_axes))
+            _nonvmapd_arr, _nonvmapd_static = partition(_nonvmapd, is_array)
+            return _vmapd, _nonvmapd_arr, Static((_nonvmapd_static, _out_axes))
 
         if len(jtu.tree_leaves(in_axes)) == 0 and self._axis_size is None:
-            vmapd, static = _fun_wrapper(dynamic_args)
+            vmapd, nonvmapd_arr, static = _fun_wrapper(dynamic_args)
             if len(jtu.tree_leaves(vmapd)) != 0:
                 raise ValueError(
                     "Cannot resolve batch dimension. Non-`None` `out_axes` requires "
                     "either `in_axes` or `axis_size` to be not `None`."
                 )
         else:
-            vmapd, static = jax.vmap(
+            vmapd, nonvmapd_arr, static = jax.vmap(
                 _fun_wrapper,
                 in_axes=(in_axes,),
-                out_axes=(0, None),
+                out_axes=(0, None, None),
                 axis_name=self._axis_name,
                 axis_size=self._axis_size,
                 **self._vmapkwargs,
             )(dynamic_args)
-        nonvmapd, out_axes = static.value
+
+        nonvmapd_static, out_axes = static.value
+        nonvmapd = combine(nonvmapd_arr, nonvmapd_static)
 
         assert jtu.tree_structure(vmapd) == jtu.tree_structure(out_axes)
         vmapd = jtu.tree_map(_swapaxes, vmapd, out_axes)
diff --git a/tests/test_module.py b/tests/test_module.py
index ff8f5e01..76996e36 100644
--- a/tests/test_module.py
+++ b/tests/test_module.py
@@ -1141,3 +1141,31 @@ class Foo3(eqx.Module):
     assert Foo1.__init__.__annotations__["x"] is Any
     assert Foo2.__init__.__annotations__["x"] is int
     assert Foo3.__init__.__annotations__["x"] is bool
+
+
+def test_no_jax_array_static():
+    class Valid(eqx.Module):
+        a: tuple
+        b: jax.Array
+
+    class InvalidTuple(eqx.Module):
+        a: tuple = eqx.field(static=True)
+        b: jax.Array
+
+    class InvalidArr(eqx.Module):
+        a: tuple
+        b: jax.Array = eqx.field(static=True)
+
+    Valid((), jnp.ones(2))
+
+    with pytest.warns(
+        UserWarning,
+        match="A JAX array is being set as static!",
+    ):
+        InvalidTuple((jnp.ones(10),), jnp.ones(10))
+
+    with pytest.warns(
+        UserWarning,
+        match="A JAX array is being set as static!",
+    ):
+        InvalidArr((), jnp.ones(10))