One of the important issues in the design of future generation of high-speed networks is to provide differentiated service to different types of traffic with various time constraints. In this paper, we study the problem of providing realtime service to either hard or soft real-time messages and normal transmission service to variable-length messages without time constraints in WDM optical networks. We propose an adaptive scheduling algorithm for scheduling message transmissions in order to improve the network performance when both real-time and non real-time messages are transmitted in one topology. We have analyzed the complexity of the algorithm to show its feasibility. We have conducted extensive discrete-event simulations to evaluate the performance of the proposed algorithm. The study suggests that when scheduling message transmission in WDM networks differentiated services should be considered in order to meet time constraints of real-time messages while non real-time messages a...