Large number of peer processes distributed in various types of networks are cooperating to achieve some objectives. The vector clock cannot be adopted to a scalable group due to communication and computation overheads. In order to reduce the overhead, we discuss a group where all the processes are synchronized by physical clocks. Here, a subgroup of processes are interconnected in a local or personal area network. Clocks of computers in every local subgroup are synchronized by using the network time protocol (NTP) with a GPS time server. The maximum time difference among clocks of computers depends on types of operating systems of the computers. Every message is given physical time when a process sends the message. We discuss a global clock group (GCG) protocol where messages are causally ordered by using the time physical stamps with maximum time difference and delay time. We evaluate the protocol in terms of the number of messages ordered compared with the vector clock.