In this paper, we consider the scheduling problem in time-division multiplexed (TDM) switching systems. In previous works, the interdependence between traffic demands in two consecutive frames is neglected, and scheduling algorithms found up to now have time complexities O(N5) or O(N4.5), where N is the switch size. However, in many applications like voice or video communications, if a source transmits a packet to a destination in a frame, it is highly probable that it will also transmit a packet to the same destination in the next frame. So it is not necessary to schedule incoming packets for every frame if we can preserve all the switching patterns for the nearest scheduled frame and update the patterns appropriately according to the changes of traffic demands. The adaptive algorithm proposed in this paper assigns time slots to packets according to the changes of traffic demands. This algorithm has the worst case time complexity O(N2 L), where L is the TDM frame length. Comparing the time complexity of the adaptive algorithm with those of previous scheduling algorithms, the adaptive algorithm can perform better than previous scheduling algorithms when N is large and/or L is small. Since traffic demands in consecutive frames are expected to be interdependent in many applications, the proposed algorithm may offer as an efficient alternative for scheduling time slots in these applications.