Abstract: A frame relay switching apparatus in a frame relay network employs a frame format used in a frame relay communication between a plurality of terminals, performed by identifying a destination by a data link connection identifier (DLCI) in an address field. Priority or non-priority information for an identifier provided in a frame being transmitted for identifying a destination terminal is registered for each DLCI so that a zone assigned to each of them is not overflown, to prevent a frame having a priority DLCI from being discarded. In case of congestion, all frames having identical non-priority DLCIs are discarded at the same time. The switching apparatus includes a plurality of transmitting buffers provided at each outgoing line, and a common buffer, which can be shared by a plurality of lines. A congested line writes a received frame in the common buffer and takes the frame out from the common buffer to write it in a respective transmitting buffer when the congestion has been resolved.