In this paper, we present a group communication protocol that achieves total ordering message delivery for mobile computing systems with multiple overlapping groups. Our mechanism is an efficient adaptation of the propagation-tree technique to the mobile computing environments. It takes advantages of the capability of stationary mobile support stations to overcome the deficiencies associated with mobile devices. We construct the propagation tree based on the stationary stations, rather than the mobile hosts. As a result, mobile hosts are relieved of the excessive load of forwarding messages and communications on wireless channels are confined to transmitting messages to destination processes. This is important considering that the bandwidth of the wireless channels is limited. Moreover, the proposed protocol employs a mechanism to synchronize transmissions within a wireless cell. This serves to avoid redundant transmissions of a message in a wireless network in an attempt to achieve better utilization of the network bandwidth. Our mechanism relies on a handoff operation to deal with mobility of mobile devices. The handoff procedure ensures a smooth integration of a mobile host into a new cell, while preserving reliability of communication and the total ordering property of message delivery.