Abstract: A switching system for switching synchronous and/or synchronous data blocks between incoming and outgoing multiplexes. The asynchronous blocks are sporadically carried in the multiplexes. The cost of the system is reduced owing to the use of a single buffer memory whose cells memorize indifferently synchronous and asynchronous blocks. The number of cells is lower than the product of the number of incoming or outgoing multiplexes and the number of blocks per frame in the multiplexes. A buffer memory managing and write addressing circuit derives and memorizes the occupied or free condition of each of the buffer memory cells thereby permanently selecting the address of one of free buffer cells in which a data block is to be written. The occupied condition of a cell is signalled responsive to the write of an incoming data block into this cell, and the free condition of the cell is signalled responsive to the last read of the written block.