diff --git a/doc/api/next_api_changes/deprecations.rst b/doc/api/next_api_changes/deprecations.rst
index 15936c9bfe5d..9dbf1691ad7d 100644
--- a/doc/api/next_api_changes/deprecations.rst
+++ b/doc/api/next_api_changes/deprecations.rst
@@ -173,3 +173,14 @@ variables is deprecated.  Additional fonts may be registered using
 ``matplotlib.compat``
 ~~~~~~~~~~~~~~~~~~~~~
 This module is deprecated.
+
+AVConv animation writer deprecated
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The ``AVConvBase``, ``AVConvWriter`` and ``AVConvFileWriter`` classes, and the
+associated ``animation.avconv_path`` and ``animation.avconv_args`` rcParams are
+deprecated.
+
+Debian 8 (2015, EOL 06/2020) and Ubuntu 14.04 (EOL 04/2019) were the
+last versions of Debian and Ubuntu to ship avconv.  It remains possible
+to force the use of avconv by using the ffmpeg-based writers with
+:rc:`animation.ffmpeg_path` set to "avconv".
diff --git a/lib/matplotlib/__init__.py b/lib/matplotlib/__init__.py
index 37f90b2929b9..323794f0632c 100644
--- a/lib/matplotlib/__init__.py
+++ b/lib/matplotlib/__init__.py
@@ -609,6 +609,8 @@ def gen_candidates():
 # listed in the rcParams (not included in _all_deprecated).
 # Values are tuples of (version,)
 _deprecated_remain_as_none = {
+    'animation.avconv_path': ('3.3',),
+    'animation.avconv_args': ('3.3',),
 }
 
 
diff --git a/lib/matplotlib/animation.py b/lib/matplotlib/animation.py
index 36fb68df82df..e53277be6e4e 100644
--- a/lib/matplotlib/animation.py
+++ b/lib/matplotlib/animation.py
@@ -644,6 +644,7 @@ def _args(self):
 
 
 # Base class of avconv information.  AVConv has identical arguments to FFMpeg.
+@cbook.deprecated('3.3')
 class AVConvBase(FFMpegBase):
     """
     Mixin class for avconv output.
diff --git a/lib/matplotlib/mpl-data/stylelib/classic.mplstyle b/lib/matplotlib/mpl-data/stylelib/classic.mplstyle
index 70b44aaab9fe..8032912a8d4c 100644
--- a/lib/matplotlib/mpl-data/stylelib/classic.mplstyle
+++ b/lib/matplotlib/mpl-data/stylelib/classic.mplstyle
@@ -478,9 +478,6 @@ animation.frame_format: png       # Controls frame format used by temp files
 animation.ffmpeg_path: ffmpeg     # Path to ffmpeg binary. Without full path
                                   # $PATH is searched
 animation.ffmpeg_args:            # Additional arguments to pass to ffmpeg
-animation.avconv_path: avconv     # Path to avconv binary. Without full path
-                                  # $PATH is searched
-animation.avconv_args:            # Additional arguments to pass to avconv
 animation.convert_path: convert   # Path to ImageMagick's convert binary.
                                   # On Windows use the full path since convert
                                   # is also the name of a system tool.
diff --git a/matplotlibrc.template b/matplotlibrc.template
index 4e6cc9d837e1..773eb8c530fa 100644
--- a/matplotlibrc.template
+++ b/matplotlibrc.template
@@ -744,9 +744,6 @@
 #animation.ffmpeg_path  : ffmpeg   ## Path to ffmpeg binary. Without full path
                                    ## $PATH is searched
 #animation.ffmpeg_args  :          ## Additional arguments to pass to ffmpeg
-#animation.avconv_path  : avconv   ## Path to avconv binary. Without full path
-                                   ## $PATH is searched
-#animation.avconv_args  :          ## Additional arguments to pass to avconv
 #animation.convert_path : convert  ## Path to ImageMagick's convert binary.
                                    ## On Windows use the full path since convert
                                    ## is also the name of a system tool.