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In distributed peer-to-peer (P2P) applications, a group of multiple peer processes (peers) are required to cooperate with each other. Messages sent by peers have to be causally delivered. In this paper, we discuss a scalable group communication protocol for a group of multiple peers in P2P overlay networks. Due to the message overhead O(n) for the number n of peers, the vector clock cannot be used to causally deliver messages is a scalable group. On the other hand, the linear clock implies the message length O(1), but some pair of messages are unnecessarily ordered. Recently, more accurate physical clocks can be used with the GPS time server and network time protocol (NTP). In this paper, we consider a group where every member peer can use a physical clock which is synchronized with the time server in the network time protocol (NTP). Even if each physical clock is synchronized with a time server, every physical clock does not show the same accurate time. The accuracy of the physical clock depends on distance to the time server, traffic in a network and operating system. In this paper, we reduce the number of messages unnecessarily ordered by taking advantage of the linear time and physical time.