Abstract: The "sunk" or "hungered" state of a process group generated at the time of resource allocation in a computer system is prevented. A corresponding relationship between processes and process groups is stored in a group managing section. Requests from processes and process groups for the allocation of a resource are stored in an exclusive control managing section together with the receiving sequence of resource allocation requests, the type of each resource allocation request and the condition of allocation of the resource. On the basis of information stored in the group managing section and the exclusive control managing section, the allocation of the resource in units of one process group and in units of one process with regard to processes belonging to the same process group is made by a process execution managing section successively in accordance with the receiving sequence.