A description is given of a protocol to handle traffic with timing constraints, such as the traffic generated by distributed real-time applications. The protocol uses a dynamic double-window based strategy to implement the optimal minimum-laxity-first policy. The author discusses the major issues involved in the design of the protocol. The tie assessment phase is formally described and its mechanism discussed. The author describes a simulation experiment that aimed at comparing the performance of the proposed scheme with the performance of the standard access mechanisms. The major advantages of the proposed protocol are the adherence of the scheme to the timing requirements of different messages and its preservation of the minimum-laxity-first policy even in the presence of ties among messages.