Contention among a plurality of synchronous and asynchronous devices connected to a shared communication medium for access to time slots in a sequence of frames is resolved by assigning a unique priority word including a priority code prefix to each device and granting access to a given slot by comparing the values of the priority words assigned to competing devices. The priority code prefix is assigned as a joint function of whether synchronous or asynchronous communication is desired and whether synchronous communication is being initiated or continued. In each assignment protocol, synchronous communication is enabled by assuring any device that initially gains access to a particular time slot continued access to the same slot in succeeding frames. If desired, devices with synchronous access may relinquish unused time slots to asynchronous traffic, while reserving the ability to resume synchronous communication.