diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 81cd11d4284d..fc35bdc5fa19 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2853,9 +2853,26 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False, **kw):
                 ('Attempting to set identical left==right results\n'
                  'in singular transformations; automatically expanding.\n'
                  'left=%s, right=%s') % (left, right))
+
         left, right = mtransforms.nonsingular(left, right, increasing=False)
         left, right = self.xaxis.limit_range_for_scale(left, right)
 
+        self._set_viewLim_intervalx(left, right, emit=emit, auto=auto)
+        return left, right
+
+    def _set_viewLim_intervalx(self, left, right, emit=True, auto=None):
+        """
+        Set the data limits for the xaxis
+        This should be the only method to change viewLim.intervalx directly.
+
+        Keyword arguments:
+          *emit*: [ *True* | *False* ]
+            Notify observers of limit change
+
+          *auto*: [ *True* | *False* | *None* ]
+            Turn *x* autoscaling on (*True*), off (*False*; default),
+            or leave unchanged (*None*)
+        """
         self.viewLim.intervalx = (left, right)
         if auto is not None:
             self._autoscaleXon = bool(auto)
@@ -2871,7 +2888,6 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False, **kw):
                             other.figure.canvas is not None):
                         other.figure.canvas.draw_idle()
         self.stale = True
-        return left, right
 
     def get_xscale(self):
         return self.xaxis.get_scale()
@@ -3115,6 +3131,22 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False, **kw):
         bottom, top = mtransforms.nonsingular(bottom, top, increasing=False)
         bottom, top = self.yaxis.limit_range_for_scale(bottom, top)
 
+        self._set_viewLim_intervaly(bottom, top, emit=emit, auto=auto)
+        return bottom, top
+
+    def _set_viewLim_intervaly(self, bottom, top, emit=True, auto=None):
+        """
+        Set the data limits for the yaxis
+        This should be the only method to change viewLim.intervaly directly.
+
+        Keyword arguments:
+          *emit*: [ *True* | *False* ]
+            Notify observers of limit change
+
+          *auto*: [ *True* | *False* | *None* ]
+            Turn *x* autoscaling on (*True*), off (*False*; default),
+            or leave unchanged (*None*)
+        """
         self.viewLim.intervaly = (bottom, top)
         if auto is not None:
             self._autoscaleYon = bool(auto)
@@ -3130,7 +3162,6 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False, **kw):
                             other.figure.canvas is not None):
                         other.figure.canvas.draw_idle()
         self.stale = True
-        return bottom, top
 
     def get_yscale(self):
         return self.yaxis.get_scale()
diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 9d600aaa0b86..82cd422e501d 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1956,15 +1956,16 @@ def set_view_interval(self, vmin, vmax, ignore=False):
 
         """
         if ignore:
-            self.axes.viewLim.intervalx = vmin, vmax
+            left, right = vmin, vmax
         else:
             Vmin, Vmax = self.get_view_interval()
             if Vmin < Vmax:
-                self.axes.viewLim.intervalx = (min(vmin, vmax, Vmin),
-                                               max(vmin, vmax, Vmax))
+                left, right = (min(vmin, vmax, Vmin),
+                               max(vmin, vmax, Vmax))
             else:
-                self.axes.viewLim.intervalx = (max(vmin, vmax, Vmin),
-                                               min(vmin, vmax, Vmax))
+                left, right = (max(vmin, vmax, Vmin),
+                               min(vmin, vmax, Vmax))
+        self.axes._set_viewLim_intervalx(left, right)
 
     def get_minpos(self):
         return self.axes.dataLim.minposx
@@ -2295,16 +2296,16 @@ def set_view_interval(self, vmin, vmax, ignore=False):
 
         """
         if ignore:
-            self.axes.viewLim.intervaly = vmin, vmax
+            bottom, top = vmin, vmax
         else:
             Vmin, Vmax = self.get_view_interval()
             if Vmin < Vmax:
-                self.axes.viewLim.intervaly = (min(vmin, vmax, Vmin),
-                                               max(vmin, vmax, Vmax))
+                bottom, top = (min(vmin, vmax, Vmin),
+                               max(vmin, vmax, Vmax))
             else:
-                self.axes.viewLim.intervaly = (max(vmin, vmax, Vmin),
-                                               min(vmin, vmax, Vmax))
-        self.stale = True
+                bottom, top = (max(vmin, vmax, Vmin),
+                               min(vmin, vmax, Vmax))
+        self.axes._set_viewLim_intervaly(bottom, top)
 
     def get_minpos(self):
         return self.axes.dataLim.minposy
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index c08d4689c57f..e8f7ce94dc9d 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -122,6 +122,19 @@ def test_twin_axis_locaters_formatters():
     ax3 = ax1.twinx()
 
 
+@cleanup
+def test_twinx_view_interval():
+    fig, ax = plt.subplots()
+    ax.set_xlim(0, 1)
+    ax.set_ylim(0, 1)
+    ax2 = ax.twinx()
+    ax3 = ax.twiny()
+    ax2.set_xticks([1, 2])
+    ax3.set_yticks([1, 2])
+    assert ax.get_xlim() == ax2.get_xlim()
+    assert ax.get_ylim() == ax3.get_ylim()
+
+
 @cleanup
 def test_twinx_cla():
     fig, ax = plt.subplots()