Minimum requirements for the high-priority token holding time (HPTHT) in a network using timed token access protocols (such as IEEE 802.4 and FDDI) are derived in order to ensure that the throughput of synchronous messages is no lower than the amount of traffic generated for that class. The minimal value is essential in order to avoid unbounded queue length for the synchronous class as well as to achieve high network responsiveness. The results have been obtained for synchronous messages generated according to a generic periodic pattern with no constraint for the shape and for the period of the pattern. The manner in which the theoretical results obtained can be used to tune the network performance is also shown