Process for transmitting compressed voice circuits over a packet switching network of the type comprising a plurality of switching nodes (SW-1 to SW-7) interconnected by connection lines and including at least an end switching node (SW-1) connected to a source exchange telephone device (PABX A) and another end switching node (SW-3) connected to a destination exchange telephone device (CX), and comprising the steps of receiving from the source exchange telephone device a sequence of uncompressed frames wherein each frame contains n slots containing each J bytes respectively associated to J voice circuits, compressing the data bits of each voice circuit in order to build a packet containing J compressed voice circuits, and providing this packet to the end switching node for transmission to the destination exchange telephone device.