Abstract: MPEG compressed video is a very important traffic type in integrated service digital networks. However, it is difficult to transmit delay and loss sensitive MPEG traffic efficiently because of its variable bit rate and bursty nature. In this paper, we introduce a new scheme for allocating resources in ATM networks, for the class of MPEG applications (e.g. medical services) with the most stringent quality of service requirements. The allocation scheme is carried out through two steps. First, calculating the required resources on a per-connection basis. Second a scheduling discipline for the UNI nodes is suggested. The remaining nodes use the simple FIFO discipline. The suggested scheme leads to a reduction of bandwidth requirements. Moreover it provides a policing mechanism for misbehaving users.