1. A process dispatching method for a multiprocessor system in which each processor of said multiprocessor system has a cache memory, said process dispatching method comprising: a first step of reading a priority and a prior processor number of a first process from a process control block of said first process, said prior processor number representing a processor of said multiprocessor system in which said first process was last executed; a second step of selecting at least one lowest priority process, said selected lowest priority process having a lowest priority among processes being executed by said processors of said multiprocessor system; a third step of discontinuing said process dispatching method when a priority of said at least one lowest priority process selected in said second step is higher than the priority of said first process; a fourth step of dispatching said first process to a processor of said multiprocessor system which is executing a lowest priority process when only one process has been selected as said lowest priority process by said second step and when a priority of said lowest priority process is lower than the priority of said first process; a fifth step of dispatching said first process to the processor indicated by said prior processor number of said first process when said prior processor number of said first process represents a processor executing said at least one lowest priority process selected by said second step; and a sixth step of dispatching said first process to a processor executing said process dispatching method when said process dispatching method is being executed by a processor of said multiprocessor system as executing a process selected as having said lowest priority by said second step.