A multiple computer system is disclosed in which the local memory of each computer (M1, M2, . . . Mn) can be different having some memory locations (A, B) which are replicated in other computers and other memory locations (E) which are not. When any computer seeks to acquire or release a synchronizing lock a check (171, 181) is made to see if the relevant memory location is present on any other machine. If yes, synchronization is carried out. However, if no, then no synchronization is required and the synchronizing procedures are by-passed.