Abstract: Method and device for managing access to the transmission medium of a multiservice distributed switching network adapted to switch traffic in synchronous circuit-switched mode and in synchronous or asynchronous packet-switched mode, the architecture of the network being based on a transmission medium time-shared between different stations characterized in that: (1) the transmission medium is synchronous and structured in frames in turn structured in time slots in turn structured in time cells, the latter being sized to contain a communication entity which can be either a circuit-switched cell or a segmented packet-switched cell, (2) an ideal time slot for access to the transmission medium in packet-switched mode is assigned to the respective stations communicating within the network, and (3) in each time cell and for all stations transmission medium access arbitration is applied to procure priority access to this medium for circuit-switched cells available at this time in any station.