A multiplex transmission apparatus is provided that conducts traffic control and discards priority control of an ATM network for transferring IP packets having a plurality of QoS conditions. The multiplex transmission apparatus includes an intermediately generated packet generator configured to generate an intermediately generated packet having second header information "CID" based on first header information "DSCP" of the IP packet, a buffer storage configured to store the intermediately generated packet in any of transmission waiting buffers based on the second header information "CID", an extractor configured to extract out the intermediately generated packet from the transmission waiting buffers according to the second header information "CID", and an ATM cell transmitter configured to load an ATM cell with the intermediately generated packet taken out and transmitting the ATM cell to the ATM network.