There is provided a power save processing method to be performed by a communication terminal capable of concurrently establishing communication links with a plurality of slave communication terminals, which reduces the transition time and provides an increased power save operation time. When a power save operation is performed at a plurality of slave communication terminals having asynchronous communication links established with the master communication terminal, the master communication terminal sets a communication start time and a communication duration for each communication link such that the communication slots used for the communication links are huddled together so as to span one continuous range, assuming that the communication links all have the same communication cycle. In accordance with the parameters thus set, the master communication terminal Negotiates with the plurality of slave communication terminals. Then, the master communication terminal itself performs a power save operation during the continuous period corresponding to unused slots which has been obtained through the above adjustments.