In an inter-subsystem communication system which has a communication queue enqueued by one subsystem having processors and dequeued by another subsystem having processors, there is provided between the subsystems direct memory access means which permits either of the subsystems to directly access a memory of the other subsystem, and in a queue element enqueued by the one subsystem is inserted memory access control information necessary for accessing the one subsystem, whereby a high-grade function is performed by the plurality of subsystems. When the source subsystem issues an enqueue command, the queue element length of a queue element produced in response to the queue command is compared with a remaining space of the queue and, if the comparison result satisfies a predetermined condition, an overflow interruption is caused in the processor of the source subsystem, thereby to efficiently detect a queue overflow state or queue usable state.