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As technologies of computer network have been advanced, appliances as well as personal computers being networked together in the home have been connected to the Internet. However, the number of IP addresses in IPv4 is estimated to be not enough in the near future. IPv4 has been thus switched with IPv6. Meanwhile, Network Address Translator (for short, NAT) has been used for solving the lack of the IP addresses. On the other hand, since a communication from the Internet to the private or home networks in NAT is difficult, many NAT traversal techniques have been developed as the solution. One of the NAT traversal techniques is that of "relaying". However, the relaying techniques have a drawback such that the relay server can be overloaded according to an increase in the number of communications. In this paper, as NAT traversal in a home gateway which is connected the home to the Internet, a scheme to balance the load by several relay servers and by a surveillance one is presented and two relay server selection methods are proposed. The proposed methods are a random selection and a priority-based one. Simulation results show that the load makes it possible to balance well in inverse proportion to the relay servers by the proposed methods.