diff --git a/tests/unit/autogram/test_engine.py b/tests/unit/autogram/test_engine.py
index 782f572c..bd3922d5 100644
--- a/tests/unit/autogram/test_engine.py
+++ b/tests/unit/autogram/test_engine.py
@@ -51,6 +51,8 @@
     WithBuffered,
     WithDropout,
     WithModuleTrackingRunningStats,
+    WithModuleWithStringArg,
+    WithModuleWithStringOutput,
     WithNoTensorOutput,
     WithRNN,
     WithSideEffect,
@@ -164,6 +166,8 @@ def test_compute_gramian(architecture: type[ShapedModule], batch_size: int, batc
         Randomness,
         WithModuleTrackingRunningStats,
         param(WithRNN, marks=mark.xfail_if_cuda),
+        WithModuleWithStringArg,
+        param(WithModuleWithStringOutput, marks=mark.xfail),
     ],
 )
 @mark.parametrize("batch_size", [1, 3, 32])
diff --git a/tests/utils/architectures.py b/tests/utils/architectures.py
index 0b26d89e..073420d2 100644
--- a/tests/utils/architectures.py
+++ b/tests/utils/architectures.py
@@ -772,6 +772,54 @@ def forward(self, input: Tensor) -> Tensor:
         return input @ self.linear.weight.T + self.linear.bias
 
 
+class WithModuleWithStringArg(ShapedModule):
+    """Model containing a module that has a string argument."""
+
+    INPUT_SHAPES = (2,)
+    OUTPUT_SHAPES = (3,)
+
+    class WithStringArg(nn.Module):
+        def __init__(self):
+            super().__init__()
+            self.matrix = nn.Parameter(torch.randn(2, 3))
+
+        def forward(self, s: str, input: Tensor) -> Tensor:
+            if s == "two":
+                return input @ self.matrix * 2.0
+            else:
+                return input @ self.matrix
+
+    def __init__(self):
+        super().__init__()
+        self.with_string_arg = self.WithStringArg()
+
+    def forward(self, input: Tensor) -> Tensor:
+        return self.with_string_arg("two", input)
+
+
+class WithModuleWithStringOutput(ShapedModule):
+    """Model containing a module that has a string output."""
+
+    INPUT_SHAPES = (2,)
+    OUTPUT_SHAPES = (3,)
+
+    class WithStringOutput(nn.Module):
+        def __init__(self):
+            super().__init__()
+            self.matrix = nn.Parameter(torch.randn(2, 3))
+
+        def forward(self, input: Tensor) -> tuple[str, Tensor]:
+            return "test", input @ self.matrix
+
+    def __init__(self):
+        super().__init__()
+        self.with_string_output = self.WithStringOutput()
+
+    def forward(self, input: Tensor) -> Tensor:
+        _, output = self.with_string_output(input)
+        return output
+
+
 class FreeParam(ShapedModule):
     """
     Model that contains a free (i.e. not contained in a submodule) parameter, that is used at the