The system according to the invention comprises a central microprocessor and peripheral microprocessors. A direct-access transfer memory is provided for the communication of the processors with one another. The memory is divided into as many distinct, determined zones as there are peripheral processors. The memory is connected to two addressing buses of which the latter serves equally well to address the boxes of the memory by the central microprocessor and to address the zones of the memory allocated to the peripheral microprocessors. The system is particularly well adapted to data transfers between a telephone automatic switch and subscribers' sets.