diff --git a/tests/test_backend.py b/tests/test_backend.py
index 225f9461a..c1bc9c052 100755
--- a/tests/test_backend.py
+++ b/tests/test_backend.py
@@ -1421,6 +1421,14 @@ def func(x1, x2):
             return tf.identity(mi, name=_TFOUTPUT)
         self._run_test_case(func, [_OUTPUT], {_INPUT: x_val1, _INPUT1: x_val2})
 
+    def test_equal_string(self):
+        x_val1 = np.array(['1'], dtype=np.string_)
+        x_val2 = np.array(['2'], dtype=np.string_)
+        def func(x1, x2):
+            mi = tf.equal(x1, x2)
+            return tf.identity(mi, name=_TFOUTPUT)
+        self._run_test_case(func, [_OUTPUT], {_INPUT: x_val1, _INPUT1: x_val2})
+
     def test_equal(self):
         x_val1 = np.array([4, 2, 4, 1], dtype=np.int32).reshape((2, 2))
         x_val2 = np.array([2, 4, 4, 1], dtype=np.int32).reshape((2, 2))
diff --git a/tf2onnx/onnx_opset/logical.py b/tf2onnx/onnx_opset/logical.py
index 6d9962ca9..3bd3be453 100644
--- a/tf2onnx/onnx_opset/logical.py
+++ b/tf2onnx/onnx_opset/logical.py
@@ -29,15 +29,21 @@ def _add_cast_to_inputs(graph, node, supported_dtypes, target_dtype):
             graph.copy_shape(inp, inp_cast.output[0])
             graph.set_dtype(inp_cast.output[0], target_dtype)
 
-
-def _add_cast_to_same_type_to_inputs(graph, node):
+def _add_cast_to_same_type_to_inputs(graph, node, supported_dtypes, target_dtype):
     common_dtype = graph.get_dtype(node.input[0])
+    if common_dtype not in supported_dtypes:
+        common_dtype = target_dtype
 
-    for inp in node.input[1:]:
+    for inp in node.input:
         if graph.get_dtype(inp) != common_dtype:
             inp_cast = graph.insert_new_node_on_input(node, "Cast", inp, to=common_dtype)
             graph.copy_shape(inp, inp_cast.output[0])
             graph.set_dtype(inp_cast.output[0], common_dtype)
+            if graph.is_const(inp) and graph.get_tensor_value(inp) == '':
+                # Convert '' string constant to -1 int
+                # https://github.com/tensorflow/tensorflow/blob/4e7f0185c70faf35e12acbfe381a729d1e6cc38c/tensorflow/python/feature_column/feature_column.py#L2286
+                const_node = graph.get_node_by_output(inp)
+                const_node.set_tensor_value(utils.np.array(-1))
 
 
 @tf_op("LogicalNot", onnx_op="Not")
@@ -92,8 +98,24 @@ def version_7(cls, ctx, node, **kwargs):
 
     @classmethod
     def version_11(cls, ctx, node, **kwargs):
-        # starting with opset-11, equal supports all types (but both operands must be of the same type)
-        _add_cast_to_same_type_to_inputs(ctx, node)
+        # starting with opset-11, equal supports all numerical types (but both operands must be of the same type)
+        # string type is not supported
+        supported_dtypes = [
+            TensorProto.BOOL,
+            TensorProto.DOUBLE,
+            TensorProto.FLOAT,
+            TensorProto.FLOAT16,
+            TensorProto.INT8,
+            TensorProto.INT16,
+            TensorProto.INT32,
+            TensorProto.INT64,
+            TensorProto.UINT8,
+            TensorProto.UINT16,
+            TensorProto.UINT32,
+            TensorProto.UINT64
+        ]
+        target_dtype = TensorProto.INT32
+        _add_cast_to_same_type_to_inputs(ctx, node, supported_dtypes, target_dtype)
         need_not = node.type == "NotEqual"
         if need_not:
             node.type = "Equal"