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In peer-to-peer (P2P) overlay networks, a group of multiple peers have to cooperate with each other. P2P systems are in nature scalable, distributed systems, where there is no centralized coordinator. Hence, a group of peers is required to be scalable in P2P overlay networks. Each peer sends a message to every peer and every other peer receives the message in a group. In group communication, each message sent by a peer is required to be causally delivered to every peer. Types of logical clocks are used to causally order messages, linear and vector clocks. The linear clock can be used in a scalable group since message length is O(1). However, some messages which are not to be causally ordered are ordered. On the other hand, all and only messages to be causally ordered are ordered in the vector clock. However, the vector clock cannot be adopted in a scalable group due to the message length O(n) for the number n of peers of the group. Recently, each computer is equipped with a physical clock which is synchronized with time servers. This means, each peer can read more correct time at a physical clock of a computer where the peer is performed. In this paper, we discuss how to causally deliver messages in a scalable group by taking advantage of linear and physical clocks. The number of messages unnecessarily ordered in the linear clock can be reduced.