When a communication system is constructed by use of a plurality of data relay apparatuses of the present invention, it is possible to control an execution/non-execution of a compression/decompression for voice data so that the compression/decompression is not repeatedly executed regardless of a PBX. An ATM multiplexer sends out a transmission pattern to an apparatus adjacent to the ATM multiplexer via a PBX, and stops the compression/decompression of the voice data to relay the voice data transmissively, only when the ATM multiplexer receives the transmission pattern from the adjacent apparatus via the PBX. In other cases, the ATM multiplexer relays the voice data while executing the compression/decompression operation for the voice data.