diff --git a/libavformat/rtsp.c b/libavformat/rtsp.c
index c079fb6293..72de537956 100644
--- a/libavformat/rtsp.c
+++ b/libavformat/rtsp.c
@@ -612,6 +612,7 @@ void ff_rtsp_close_streams(AVFormatContext *s)
 static void *rtsp_rtp_mux_open(AVFormatContext *s, AVStream *st,
                                URLContext *handle)
 {
+    RTSPState *rt = s->priv_data;
     AVFormatContext *rtpctx;
     int ret;
     AVOutputFormat *rtp_format = av_guess_format("rtp", NULL, NULL);
@@ -634,6 +635,9 @@ static void *rtsp_rtp_mux_open(AVFormatContext *s, AVStream *st,
     /* Copy other stream parameters. */
     rtpctx->streams[0]->sample_aspect_ratio = st->sample_aspect_ratio;
 
+    /* Set the synchronized start time. */
+    rtpctx->start_time_realtime = rt->start_time;
+
     /* Remove the local codec, link to the original codec
      * context instead, to give the rtp muxer access to
      * codec parameters. */
@@ -1340,6 +1344,8 @@ static int rtsp_setup_output_streams(AVFormatContext *s, const char *addr)
     char *sdp;
     AVFormatContext sdp_ctx, *ctx_array[1];
 
+    rt->start_time = av_gettime();
+
     /* Announce the stream */
     snprintf(cmd, sizeof(cmd),
              "ANNOUNCE %s RTSP/1.0\r\n"
diff --git a/libavformat/rtsp.h b/libavformat/rtsp.h
index 01caf39bf9..a322281282 100644
--- a/libavformat/rtsp.h
+++ b/libavformat/rtsp.h
@@ -271,6 +271,9 @@ typedef struct RTSPState {
      * for all subsequent RTSP requests, rather than the input URI; in
      * other cases, this is a copy of AVFormatContext->filename. */
     char control_uri[1024];
+
+    /** The synchronized start time of the output streams. */
+    int64_t start_time;
 } RTSPState;
 
 /**