diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 18d54b658ea9..886a544251cc 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1434,6 +1434,13 @@ def update_units(self, data):
         if converter is None:
             return False
 
+        if (self.converter is not None) and (self.converter != converter):
+            raise TypeError('Attempting to plot data that is '
+                            'registered to be converted with %s but '
+                            'is incompatible with existing axis data '
+                            'converter %s' % (converter.__class__,
+                                self.converter.__class__))
+
         neednew = self.converter != converter
         self.converter = converter
         default = self.converter.default_units(data, self)
diff --git a/lib/matplotlib/tests/test_dates.py b/lib/matplotlib/tests/test_dates.py
index 437482f5fa2e..e457532fd4aa 100644
--- a/lib/matplotlib/tests/test_dates.py
+++ b/lib/matplotlib/tests/test_dates.py
@@ -477,3 +477,14 @@ def test_tz_utc():
 def test_num2timedelta(x, tdelta):
     dt = mdates.num2timedelta(x)
     assert dt == tdelta
+
+
+def test_one_non_None_converter():
+    # test that we only allow one non-None converter at once:
+    base = datetime.datetime(2017, 1, 1, 0, 10, 0)
+    time = [base - datetime.timedelta(days=x) for x in range(0, 3)]
+    data = [0., 2., 4.]
+    fig, ax = plt.subplots()
+    ax.plot(time, data)
+    with pytest.raises(TypeError):
+        ax.plot(['a', 'b'], [1., 2.])