A method and an equipment for prioritizing traffic in an ATM network, in which services of the network are divided into different service classes, and cells are transmitted via service-class-specific buffers, whereby a cell is temporarily stored in the buffer corresponding to the service class of said cell. In order to be able to pay as much attention as possible to the application of the subscriber at the time in question and at the same time retain the trunk network as simple as possible, the service class division is implemented at least at an NNI interface of the network only by means of a virtual path identifier (VPI) in the header of the cell so that one service class corresponds to each identifier and a certain group of virtual path identifiers belongs to the same service class.