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The asynchronous PS (Power-Saving) protocol was designed to synchronize two wireless hosts in the asynchronous ad hoc network such that those two wireless hosts can transmit an unicast message even though they have asynchronous wakeup frequencies. However, for transmitting a multicast message to more than one receiver, the protocol could not guarantee that all receivers can wake up simultaneously and then receive the multicast message. In this paper, we propose a new asynchronous PS protocol, named CRT-MAC PS protocol, for the multicast transmission in the asynchronous ad hoc networks. We define the difference m-pair property to guarantee that m different wakeup frequencies have the intersection. Thus, m wireless hosts with m different wakeup frequencies satisfying the difference m-pair property could wake up simultaneously. The CRT-MAC PS protocol utilizes the concept of Chinese Remainder Theorem to generate m wakeup frequencies which satisfy the difference m-pair property. When m wireless hosts use the wakeup frequency generated by the Chinese Remainder Theorem to transmit the multicast message, they will wake up simultaneously and receive the multicast message.