diff --git a/pandas/tests/reshape/concat/test_categorical.py b/pandas/tests/reshape/concat/test_categorical.py
index 5bafd2e8e8503..c2030828d1cac 100644
--- a/pandas/tests/reshape/concat/test_categorical.py
+++ b/pandas/tests/reshape/concat/test_categorical.py
@@ -1,3 +1,5 @@
+from datetime import datetime
+
 import numpy as np
 
 from pandas.core.dtypes.dtypes import CategoricalDtype
@@ -203,6 +205,32 @@ def test_categorical_concat_gh7864(self):
         dfa = df1._append(df2)
         tm.assert_index_equal(df["grade"].cat.categories, dfa["grade"].cat.categories)
 
+    def test_categorical_datetime_concat(self):
+        # GH 39443
+        # test catergorical dataframes both containing datetimes
+        df1 = DataFrame(
+            {"x": Series(datetime(2021, 1, 1), index=[0], dtype="category")}
+        )
+        df2 = DataFrame(
+            {"x": Series(datetime(2021, 1, 2), index=[1], dtype="category")}
+        )
+        expected = DataFrame(
+            {"x": Series([datetime(2021, 1, 1), datetime(2021, 1, 2)])}
+        )
+        result = pd.concat([df1, df2])
+        tm.assert_equal(result, expected)
+
+    def test_categorical_datetime_and_string_concat(self):
+        # GH 39443
+        # test catergorical dataframes one with datetime, one with a string
+        df1 = DataFrame(
+            {"x": Series(datetime(2021, 1, 1), index=[0], dtype="category")}
+        )
+        df2 = DataFrame({"x": Series("test string", index=[1], dtype="category")})
+        expected = DataFrame({"x": Series([datetime(2021, 1, 1), "test string"])})
+        result = pd.concat([df1, df2])
+        tm.assert_equal(result, expected)
+
     def test_categorical_index_upcast(self):
         # GH 17629
         # test upcasting to object when concatinating on categorical indexes