diff --git a/doc/users/next_whats_new/2019-02-27-AL.rst b/doc/users/next_whats_new/2019-02-27-AL.rst
new file mode 100644
index 000000000000..f6d1779f150a
--- /dev/null
+++ b/doc/users/next_whats_new/2019-02-27-AL.rst
@@ -0,0 +1,5 @@
+Unit converters now handle instances of subclasses
+``````````````````````````````````````````````````
+
+Unit converters now also handle instances of subclasses of the class they have
+been registered for.
diff --git a/lib/matplotlib/tests/test_units.py b/lib/matplotlib/tests/test_units.py
index 58b225aa3482..e9ce737385a3 100644
--- a/lib/matplotlib/tests/test_units.py
+++ b/lib/matplotlib/tests/test_units.py
@@ -1,10 +1,11 @@
+from datetime import datetime
+import platform
 from unittest.mock import MagicMock
 
 import matplotlib.pyplot as plt
-from matplotlib.testing.decorators import image_comparison
+from matplotlib.testing.decorators import check_figures_equal, image_comparison
 import matplotlib.units as munits
 import numpy as np
-import platform
 import pytest
 
 
@@ -119,7 +120,6 @@ def test_empty_set_limits_with_units(quantity_converter):
 @image_comparison(['jpl_bar_units.png'],
                   savefig_kwarg={'dpi': 120}, style='mpl20')
 def test_jpl_bar_units():
-    from datetime import datetime
     import matplotlib.testing.jpl_units as units
     units.register()
 
@@ -136,7 +136,6 @@ def test_jpl_bar_units():
 @image_comparison(['jpl_barh_units.png'],
                   savefig_kwarg={'dpi': 120}, style='mpl20')
 def test_jpl_barh_units():
-    from datetime import datetime
     import matplotlib.testing.jpl_units as units
     units.register()
 
@@ -164,3 +163,12 @@ def test_scatter_element0_masked():
     fig, ax = plt.subplots()
     ax.scatter(times, y)
     fig.canvas.draw()
+
+
+@check_figures_equal(extensions=["png"])
+def test_subclass(fig_test, fig_ref):
+    class subdate(datetime):
+        pass
+
+    fig_test.subplots().plot(subdate(2000, 1, 1), 0, "o")
+    fig_ref.subplots().plot(datetime(2000, 1, 1), 0, "o")
diff --git a/lib/matplotlib/units.py b/lib/matplotlib/units.py
index b5c9f724b44e..a6186a4eb59f 100644
--- a/lib/matplotlib/units.py
+++ b/lib/matplotlib/units.py
@@ -205,18 +205,20 @@ def get_converter(self, x):
             # If there are no elements in x, infer the units from its dtype
             if not x.size:
                 return self.get_converter(np.array([0], dtype=x.dtype))
-        try:  # Look up in the cache.
-            return self[type(x)]
-        except KeyError:
-            try:  # If cache lookup fails, look up based on first element...
-                first = cbook.safe_first_element(x)
-            except (TypeError, StopIteration):
+        for cls in type(x).__mro__:  # Look up in the cache.
+            try:
+                return self[cls]
+            except KeyError:
                 pass
-            else:
-                # ... and avoid infinite recursion for pathological iterables
-                # where indexing returns instances of the same iterable class.
-                if type(first) is not type(x):
-                    return self.get_converter(first)
+        try:  # If cache lookup fails, look up based on first element...
+            first = cbook.safe_first_element(x)
+        except (TypeError, StopIteration):
+            pass
+        else:
+            # ... and avoid infinite recursion for pathological iterables for
+            # which indexing returns instances of the same iterable class.
+            if type(first) is not type(x):
+                return self.get_converter(first)
         return None