Wireless data communication system having power saving function

A wireless data communication system is operable in a power saving mode wherein stations are synchronized to be in an awake state to receive synchronizing messages (TIM,PSYNC) and traffic indicator information and are changed to a doze state if they are not to receive data messages. In one embodiment all stations(20) communicate via a base station access point (16), which broadcasts synchronizing messages (TIM) at regular intervals identifying stations (20) that are to receive data messages. In another embodiment all stations (220) communicate directly with one another, one station assumes the role of a master station and broadcasts synchronizing messages (PSYNC), and stations (220) desiring to transmit data messages transmit traffic indicator messages (PTIM) to the appropriate destination stations (220), in a synchronized awake period just before the next synchronizing message (PSYNC) is expected to arrive.