diff --git a/doc/api/next_api_changes/2018-02-15-AL.rst b/doc/api/next_api_changes/2018-02-15-AL.rst
@@ -0,0 +1,17 @@
+Axis-dependent Locators and Formatters explicitly error out when used over multiple Axis
+````````````````````````````````````````````````````````````````````````````````````````
+
+Certain Locators and Formatters (e.g. the default `AutoLocator` and
+`ScalarFormatter`) can only be used meaningfully on one Axis object at a time
+(i.e., attempting to use a single `AutoLocator` instance on the x and the y
+axis of an Axes, or the x axis of two different Axes, would result in
+nonsensical results).
+
+Such "double-use" is now detected and raises a RuntimeError *at canvas draw
+time*.  The exception is not raised when the second Axis is registered in order
+to avoid incorrectly raising exceptions for the Locators and Formatters that
+*can* be used on multiple Axis objects simultaneously (e.g. `NullLocator` and
+`FuncFormatter`).
+
+In case a Locator or a Formatter really needs to be reassigned from one axis to
+another, first set its axis to None to bypass this protection.
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
@@ -1589,11 +1589,19 @@ def subplots(self, nrows=1, ncols=1, sharex=False, sharey=False,
             return axarr
 
     def _remove_ax(self, ax):
-        def _reset_loc_form(axis):
-            axis.set_major_formatter(axis.get_major_formatter())
-            axis.set_major_locator(axis.get_major_locator())
-            axis.set_minor_formatter(axis.get_minor_formatter())
-            axis.set_minor_locator(axis.get_minor_locator())
+        def _reset_tickers(axis):
+            major_formatter = axis.get_major_formatter()
+            major_formatter.set_axis(None)  # Bypass prevention of axis reset.
+            axis.set_major_formatter(major_formatter)
+            major_locator = axis.get_major_locator()
+            major_locator.set_axis(None)
+            axis.set_major_locator(major_locator)
+            minor_formatter = axis.get_minor_formatter()
+            minor_formatter.set_axis(None)
+            axis.set_minor_formatter(minor_formatter)
+            minor_locator = axis.get_minor_locator()
+            minor_locator.set_axis(None)
+            axis.set_minor_locator(minor_locator)
 
         def _break_share_link(ax, grouper):
             siblings = grouper.get_siblings(ax)
@@ -1607,11 +1615,11 @@ def _break_share_link(ax, grouper):
         self.delaxes(ax)
         last_ax = _break_share_link(ax, ax._shared_y_axes)
         if last_ax is not None:
-            _reset_loc_form(last_ax.yaxis)
+            _reset_tickers(last_ax.yaxis)
 
         last_ax = _break_share_link(ax, ax._shared_x_axes)
         if last_ax is not None:
-            _reset_loc_form(last_ax.xaxis)
+            _reset_tickers(last_ax.xaxis)
 
     def clf(self, keep_observers=False):
         """

diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
@@ -198,6 +198,14 @@ class _AxisWrapper(object):
     def __init__(self, axis):
         self._axis = axis
 
+    def __eq__(self, other):
+        # Needed so that assignment, as the locator.axis attribute, of another
+        # _AxisWrapper wrapping the same axis works.
+        return self._axis == other._axis
+
+    def __hash__(self):
+        return hash((type(self), *sorted(vars(self).items())))
+
     def get_view_interval(self):
         return np.rad2deg(self._axis.get_view_interval())
 
@@ -227,10 +235,11 @@ class ThetaLocator(mticker.Locator):
     """
     def __init__(self, base):
         self.base = base
-        self.axis = self.base.axis = _AxisWrapper(self.base.axis)
+        self.set_axis(self.base.axis)
 
     def set_axis(self, axis):
-        self.axis = _AxisWrapper(axis)
+        super().set_axis(_AxisWrapper(axis))
+        self.base.set_axis(None)  # Bypass prevention of axis resetting.
         self.base.set_axis(self.axis)
 
     def __call__(self):
@@ -383,7 +392,6 @@ def _wrap_locator_formatter(self):
     def cla(self):
         super().cla()
         self.set_ticks_position('none')
-        self._wrap_locator_formatter()
 
     def _set_scale(self, value, **kwargs):
         super()._set_scale(value, **kwargs)

diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
@@ -897,3 +897,29 @@ def minorticksubplot(xminor, yminor, i):
     minorticksubplot(True, False, 2)
     minorticksubplot(False, True, 3)
     minorticksubplot(True, True, 4)
+
+
+def test_multiple_assignment():
+    fig = plt.figure()
+
+    ax = fig.subplots()
+    fmt = mticker.NullFormatter()
+    ax.xaxis.set_major_formatter(fmt)
+    ax.yaxis.set_major_formatter(fmt)
+    fig.canvas.draw()  # No error.
+    fig.clf()
+
+    ax = fig.subplots()
+    fmt = mticker.ScalarFormatter()
+    ax.xaxis.set_major_formatter(fmt)
+    ax.xaxis.set_minor_formatter(fmt)
+    fig.canvas.draw()  # No error.
+    fig.clf()
+
+    ax = fig.subplots()
+    fmt = mticker.ScalarFormatter()
+    ax.xaxis.set_major_formatter(fmt)
+    ax.yaxis.set_major_formatter(fmt)
+    with pytest.raises(RuntimeError):
+        fig.canvas.draw()
+    fig.clf()
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
@@ -217,11 +217,41 @@ def get_tick_space(self):
         return 9
 
 
-class TickHelper(object):
-    axis = None
+class TickHelper:
+    # TickHelpers that access their axis attribute can only be assigned to
+    # one Axis at a time, but we don't know a priori whether they will (e.g.,
+    # NullFormatter doesn't, but ScalarFormatter does).  So keep track of all
+    # Axises that a TickHelper is assigned to (in a set: a TickHelper could be
+    # assigned both as major and minor helper on a single axis), but only error
+    # out after multiple assignment when the attribute is accessed.
 
-    def set_axis(self, axis):
-        self.axis = axis
+    # As an escape hatch, allow resetting the axis by first setting it to None.
+
+    @property
+    def axis(self):
+        # We can't set the '_set_axises' attribute in TickHelper.__init__
+        # (without a deprecation period) because subclasses didn't have to call
+        # super().__init__ so far so they likely didn't.
+        set_axises = getattr(self, "_set_axises", set())
+        if len(set_axises) == 0:
+            return None
+        elif len(set_axises) == 1:
+            axis, = set_axises
+            return axis
+        else:
+            raise RuntimeError(
+                f"The 'axis' attribute of this {type(self).__name__} object "
+                f"has been set multiple times, but a {type(self).__name__} "
+                f"can only be used for one Axis at a time")
+
+    @axis.setter
+    def axis(self, axis):
+        if not hasattr(self, "_set_axises") or axis is None:
+            self._set_axises = set()
+        if axis is not None:
+            self._set_axises.add(axis)
+
+    set_axis = axis.fset
 
     def create_dummy_axis(self, **kwargs):
         if self.axis is None: