diff --git a/doc/APIchanges b/doc/APIchanges
index 38c1be61c7..87ff51bdc2 100644
--- a/doc/APIchanges
+++ b/doc/APIchanges
@@ -15,6 +15,12 @@ libavutil:     2017-10-21
 
 API changes, most recent first:
 
+2017-xx-xx - xxxxxxx - lavf 58.3.101 - avformat.h
+  Explicitly make avformat_network_init() and avformat_network_deinit() optional.
+  If these are not called, network initialization and deinitialization is
+  automatic, and unlike in older versions, fully supported, unless libavformat
+  is linked to ancient GnuTLS and OpenSSL.
+
 2017-xx-xx - xxxxxxx - lavr 4.0.0 - avresample.h
   Deprecate the entire library. Merged years ago to provide compatibility
   with Libav, it remained unmaintained by the FFmpeg project and duplicated
diff --git a/libavformat/avformat.h b/libavformat/avformat.h
index 4f2798a871..9de851fcc5 100644
--- a/libavformat/avformat.h
+++ b/libavformat/avformat.h
@@ -1993,17 +1993,24 @@ void av_register_input_format(AVInputFormat *format);
 void av_register_output_format(AVOutputFormat *format);
 
 /**
- * Do global initialization of network components. This is optional,
- * but recommended, since it avoids the overhead of implicitly
- * doing the setup for each session.
+ * Do global initialization of network libraries. This is optional,
+ * and not recommended anymore.
  *
- * Calling this function will become mandatory if using network
- * protocols at some major version bump.
+ * This functions only exists to work around thread-safety issues
+ * with older GnuTLS or OpenSSL libraries. If libavformat is linked
+ * to newer versions of those libraries, or if you do not use them,
+ * calling this function is unnecessary. Otherwise, you need to call
+ * this function before any other threads using them are started.
+ *
+ * This function will be deprecated once support for older GnuTLS and
+ * OpenSSL libraries is removed, and this function has no purpose
+ * anymore.
  */
 int avformat_network_init(void);
 
 /**
- * Undo the initialization done by avformat_network_init.
+ * Undo the initialization done by avformat_network_init. Call it only
+ * once for each time you called avformat_network_init.
  */
 int avformat_network_deinit(void);
 
diff --git a/libavformat/network.c b/libavformat/network.c
index e9eb4b443a..d5c82e9ab9 100644
--- a/libavformat/network.c
+++ b/libavformat/network.c
@@ -54,20 +54,11 @@ void ff_tls_deinit(void)
 #endif
 }
 
-int ff_network_inited_globally;
-
 int ff_network_init(void)
 {
 #if HAVE_WINSOCK2_H
     WSADATA wsaData;
-#endif
 
-    if (!ff_network_inited_globally)
-        av_log(NULL, AV_LOG_WARNING, "Using network protocols without global "
-                                     "network initialization. Please use "
-                                     "avformat_network_init(), this will "
-                                     "become mandatory later.\n");
-#if HAVE_WINSOCK2_H
     if (WSAStartup(MAKEWORD(1,1), &wsaData))
         return 0;
 #endif
diff --git a/libavformat/network.h b/libavformat/network.h
index a663115541..22a4fb8950 100644
--- a/libavformat/network.h
+++ b/libavformat/network.h
@@ -75,7 +75,6 @@ int ff_neterrno(void);
 
 int ff_socket_nonblock(int socket, int enable);
 
-extern int ff_network_inited_globally;
 int ff_network_init(void);
 void ff_network_close(void);
 
diff --git a/libavformat/utils.c b/libavformat/utils.c
index 2185a6f05b..51a510cbb7 100644
--- a/libavformat/utils.c
+++ b/libavformat/utils.c
@@ -4873,7 +4873,6 @@ int avformat_network_init(void)
 {
 #if CONFIG_NETWORK
     int ret;
-    ff_network_inited_globally = 1;
     if ((ret = ff_network_init()) < 0)
         return ret;
     if ((ret = ff_tls_init()) < 0)
@@ -4887,7 +4886,6 @@ int avformat_network_deinit(void)
 #if CONFIG_NETWORK
     ff_network_close();
     ff_tls_deinit();
-    ff_network_inited_globally = 0;
 #endif
     return 0;
 }
diff --git a/libavformat/version.h b/libavformat/version.h
index 5ced041f0a..6453d4559f 100644
--- a/libavformat/version.h
+++ b/libavformat/version.h
@@ -33,7 +33,7 @@
 // Also please add any ticket numbers that you believe might be affected here
 #define LIBAVFORMAT_VERSION_MAJOR  58
 #define LIBAVFORMAT_VERSION_MINOR   3
-#define LIBAVFORMAT_VERSION_MICRO 100
+#define LIBAVFORMAT_VERSION_MICRO 101
 
 #define LIBAVFORMAT_VERSION_INT AV_VERSION_INT(LIBAVFORMAT_VERSION_MAJOR, \
                                                LIBAVFORMAT_VERSION_MINOR, \
