The paper proposes a new mechanism for group communication which guarantees the total ordering of message delivery, especially the ordering on the members common to overlapping groups. The mechanism is based on a method which propagates messages to all destinations along trees. The approach has the following advantages over the propagation tree mechanism: (1) greater parallelism (messages can be sent to destinations by using broadcast networks); (2) less latency time (it takes less time to have a message reach all the destinations); and (3) more flexible to dynamic membership changes, (each change of process membership does not involve a restructuring of propagation trees).>