diff --git a/gst-libs/gst/codecparsers/gsth264parser.c b/gst-libs/gst/codecparsers/gsth264parser.c
index 012f1d0d73..68aa25068a 100644
--- a/gst-libs/gst/codecparsers/gsth264parser.c
+++ b/gst-libs/gst/codecparsers/gsth264parser.c
@@ -1556,6 +1556,14 @@ gst_h264_parser_identify_nalu_avc (GstH264NalParser * nalparser,
 
   memset (nalu, 0, sizeof (*nalu));
 
+  /* Would overflow guint below otherwise: the callers needs to ensure that
+   * this never happens */
+  if (offset > G_MAXUINT32 - nal_length_size) {
+    GST_WARNING ("offset + nal_length_size overflow");
+    nalu->size = 0;
+    return GST_H264_PARSER_BROKEN_DATA;
+  }
+
   if (size < offset + nal_length_size) {
     GST_DEBUG ("Can't parse, buffer has too small size %" G_GSIZE_FORMAT
         ", offset %u", size, offset);
@@ -1570,7 +1578,13 @@ gst_h264_parser_identify_nalu_avc (GstH264NalParser * nalparser,
   nalu->sc_offset = offset;
   nalu->offset = offset + nal_length_size;
 
-  if (size < nalu->size + nal_length_size) {
+  if (nalu->size > G_MAXUINT32 - nal_length_size) {
+    GST_WARNING ("NALU size + nal_length_size overflow");
+    nalu->size = 0;
+    return GST_H264_PARSER_BROKEN_DATA;
+  }
+
+  if (size < (gsize) nalu->size + nal_length_size) {
     nalu->size = 0;
 
     return GST_H264_PARSER_NO_NAL_END;
diff --git a/gst-libs/gst/codecparsers/gsth265parser.c b/gst-libs/gst/codecparsers/gsth265parser.c
index 6c17593315..99cb232285 100644
--- a/gst-libs/gst/codecparsers/gsth265parser.c
+++ b/gst-libs/gst/codecparsers/gsth265parser.c
@@ -1531,6 +1531,14 @@ gst_h265_parser_identify_nalu_hevc (GstH265Parser * parser,
 
   memset (nalu, 0, sizeof (*nalu));
 
+  /* Would overflow guint below otherwise: the callers needs to ensure that
+   * this never happens */
+  if (offset > G_MAXUINT32 - nal_length_size) {
+    GST_WARNING ("offset + nal_length_size overflow");
+    nalu->size = 0;
+    return GST_H265_PARSER_BROKEN_DATA;
+  }
+
   if (size < offset + nal_length_size) {
     GST_DEBUG ("Can't parse, buffer has too small size %" G_GSIZE_FORMAT
         ", offset %u", size, offset);
@@ -1545,7 +1553,13 @@ gst_h265_parser_identify_nalu_hevc (GstH265Parser * parser,
   nalu->sc_offset = offset;
   nalu->offset = offset + nal_length_size;
 
-  if (size < nalu->size + nal_length_size) {
+  if (nalu->size > G_MAXUINT32 - nal_length_size) {
+    GST_WARNING ("NALU size + nal_length_size overflow");
+    nalu->size = 0;
+    return GST_H265_PARSER_BROKEN_DATA;
+  }
+
+  if (size < (gsize) nalu->size + nal_length_size) {
     nalu->size = 0;
 
     return GST_H265_PARSER_NO_NAL_END;
diff --git a/tests/check/libs/h264parser.c b/tests/check/libs/h264parser.c
index c7c46d9a20..d322dd8db0 100644
--- a/tests/check/libs/h264parser.c
+++ b/tests/check/libs/h264parser.c
@@ -229,6 +229,65 @@ GST_START_TEST (test_h264_parse_slice_5bytes)
 
 GST_END_TEST;
 
+GST_START_TEST (test_h264_parse_identify_nalu_avc)
+{
+  GstH264ParserResult res;
+  GstH264NalUnit nalu;
+  GstH264NalParser *const parser = gst_h264_nal_parser_new ();
+  /* Skip 3 bytes for the start code */
+  const gsize nal_size = sizeof (slice_dpa) - 3;
+  const gsize buf_size = 4 + nal_size;
+  guint8 *buf = g_new (guint8, buf_size);
+
+  memcpy (buf + 4, slice_dpa + 3, nal_size);
+
+  GST_WRITE_UINT16_BE (buf + 2, nal_size);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 2, buf_size, 2, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_OK);
+  assert_equals_int (nalu.type, GST_H264_NAL_SLICE_DPA);
+  assert_equals_int (nalu.offset, 4);
+  assert_equals_int (nalu.size, nal_size);
+
+  GST_WRITE_UINT32_BE (buf, nal_size);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_OK);
+  assert_equals_int (nalu.type, GST_H264_NAL_SLICE_DPA);
+  assert_equals_int (nalu.offset, 4);
+  assert_equals_int (nalu.size, nal_size);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 2);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 3);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 4);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_NO_NAL_END);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 6);
+  res = gst_h264_parser_identify_nalu_avc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H264_PARSER_NO_NAL_END);
+
+  g_free (buf);
+  gst_h264_nal_parser_free (parser);
+}
+
+GST_END_TEST;
+
 static guint8 nalu_sps_with_vui[] = {
   0x00, 0x00, 0x00, 0x01, 0x67, 0x64, 0x00, 0x28,
   0xac, 0xd9, 0x40, 0x78, 0x04, 0x4f, 0xde, 0x03,
@@ -666,6 +725,7 @@ h264parser_suite (void)
   tcase_add_test (tc_chain, test_h264_parse_slice_dpa);
   tcase_add_test (tc_chain, test_h264_parse_slice_eoseq_slice);
   tcase_add_test (tc_chain, test_h264_parse_slice_5bytes);
+  tcase_add_test (tc_chain, test_h264_parse_identify_nalu_avc);
   tcase_add_test (tc_chain, test_h264_parse_invalid_sei);
   tcase_add_test (tc_chain, test_h264_create_sei);
 
diff --git a/tests/check/libs/h265parser.c b/tests/check/libs/h265parser.c
index 449fe2fae8..ff175987e0 100644
--- a/tests/check/libs/h265parser.c
+++ b/tests/check/libs/h265parser.c
@@ -255,6 +255,65 @@ GST_START_TEST (test_h265_parse_slice_6bytes)
 
 GST_END_TEST;
 
+GST_START_TEST (test_h265_parse_identify_nalu_hevc)
+{
+  GstH265ParserResult res;
+  GstH265NalUnit nalu;
+  GstH265Parser *parser = gst_h265_parser_new ();
+  /* Skip 4 bytes for the start code */
+  const gsize nal_size = sizeof (slice_eos_slice_eob) - 4;
+  const gsize buf_size = 4 + nal_size;
+  guint8 *buf = g_new (guint8, buf_size);
+
+  memcpy (buf + 4, slice_eos_slice_eob + 4, nal_size);
+
+  GST_WRITE_UINT16_BE (buf + 2, nal_size);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 2, buf_size, 2, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_OK);
+  assert_equals_int (nalu.type, GST_H265_NAL_SLICE_IDR_W_RADL);
+  assert_equals_int (nalu.offset, 4);
+  assert_equals_int (nalu.size, nal_size);
+
+  GST_WRITE_UINT32_BE (buf, nal_size);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_OK);
+  assert_equals_int (nalu.type, GST_H265_NAL_SLICE_IDR_W_RADL);
+  assert_equals_int (nalu.offset, 4);
+  assert_equals_int (nalu.size, nal_size);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 2);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 3);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_BROKEN_DATA);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 4);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_NO_NAL_END);
+
+  GST_WRITE_UINT32_BE (buf, G_MAXUINT32 - 6);
+  res = gst_h265_parser_identify_nalu_hevc (parser, buf, 0, buf_size, 4, &nalu);
+
+  assert_equals_int (res, GST_H265_PARSER_NO_NAL_END);
+
+  g_free (buf);
+  gst_h265_parser_free (parser);
+}
+
+GST_END_TEST;
+
 GST_START_TEST (test_h265_base_profiles)
 {
   GstH265ProfileTierLevel ptl;
@@ -1118,6 +1177,7 @@ h265parser_suite (void)
   tcase_add_test (tc_chain, test_h265_parse_slice_eos_slice_eob);
   tcase_add_test (tc_chain, test_h265_parse_pic_timing);
   tcase_add_test (tc_chain, test_h265_parse_slice_6bytes);
+  tcase_add_test (tc_chain, test_h265_parse_identify_nalu_hevc);
   tcase_add_test (tc_chain, test_h265_base_profiles);
   tcase_add_test (tc_chain, test_h265_base_profiles_compat);
   tcase_add_test (tc_chain, test_h265_format_range_profiles_exact_match);