In a game system of the illustrative embodiments, a slave machine a process of lengthening a frame cycle at times k1 and k2 by a time period of j1 and a time period of j2, respectively, thereby establishing synchronization with a master machine. Also, the master machine carries out a process of lengthening the frame cycle thereof by a time period of i at time h1 to deliberately cause the frame cycle to tend to be slower than the frame cycle of the slave machine, thereby causing the slave machine to adjust the frame cycle thereof so as to be lengthened by a time period of j3 at time k3. Accordingly, it is possible to secure a minimum length of the process cycle with consideration of an individual difference between game apparatuses