Distributed applications are realized by the cooperation of a group of multiple objects. In the group cooperation, objects send and receive messages in various ways. A message is multicast to objects in the group. In addition, multiple types of messages are sent in parallel to multiple destinations. Then, an object waits for messages from all objects and some of the source objects, i.e., in conjunctive and disjunctive ways. In this paper, we define a novel precedent relation on request and response messages exchanged among objects in the presence of the transmission and receipt methods. We present a communication protocol for supporting a group of processes with the ordered delivery of messages in the precedent relation. By using the protocol, it is easy to realize distributed object-based applications like database replications.