An apparatus for processing a speech signal includes a receiver, a speech signal decoder, a speech rate conversion information detector, and a speech rate converting processor. The receiver receives multiplexed signal of information concerning controls and programs, including speech packets through a transmission line. The decoder decodes the speech signal of packets out of the received signals. The detector detects speech rate conversion execution information in the received signals. The processor subjects the decoded speech signal to a speech rate conversion process if the speech rate conversion execution information indicates that the speech signal has not been subjected to the speech rate conversion process on the transmitting end, and which does not subject the decoded speech signal to the speech rate conversion process if the speech rate conversion execution information indicates that the speech signal has been subjected to the speech rate conversion process on the transmitting end.