A distributed demand assigned multiple access control scheme for use in connection with a processing satellite communications system, where multiple users are assigned to a common transmission resource as part of a sharing set. The control scheme of the invention makes use of a reservation procedure by transmitting set addressed reservation messages in a contentious control flow to reserve data transfer time in a non-contentious main flow. Each user of the sharing set is synchronized to the next available uplink time slot available to transmit data in the main flow. If a transmitted reservation message is returned in the satellite downlink, the terminal knows that all of the users of the set received the message. That reserved time interval in the main flow Is now owned by that user, and each user in the shared set updates its next available uplink time slot based on the reserved time.