One or more interrogating commander stations and an unknown plurality of responding responder stations coordinate use of a common communication medium. Each commander station and each responder station is equipped to broadcast messages and to check for error in received messages. When more than one station attempts to broadcast simultaneously, an erroneous message is received and communication is interrupted. To establish uninterrupted communication, a commander station broadcasts a command causing each responder station of a potentially large first number of responder stations to each select a random number from a known range and retain it as its arbitration number. After receipt of such a command, each addressed responder station transmits a response message containing its arbitration number. Zero, one, or several responses may occur simultaneously. By broadcasting requests for identification to various subsets of the full range of arbitration numbers and checking for an immediate error-free response, a commander station can determine the arbitration number of every responder station capable of communicating at the time. Consequently, a commander station can conduct subsequent uninterrupted communication with each responder station, for example by addressing only one responder station. Responder stations of this invention require minimal logic and circuitry to respond to multiple commander stations.