Asynchronous Transfer Mode (ATM) networks can support different traffic classes with diverse flow characteristics and guarantee the different quality of service (QoS) requirements. In this paper, both cell loss probability and maximum cell delay of each traffic class are considered. By exten-ding the Markov Modulated Deterministic Process method to the case of heterogeneous traffic, we develop an efficient algorithm to compute the minimum capacity required to satisfy all the QoS requirements when multiple classes of traffic sources are multi-plexed onto a virtual path (VP). Using the developed algorithm, we propose an iterative method to search for the optimal static VP bandwidth allocation. We then compare the performance of the static schemes to that of a dynamic VP bandwidth allocation scheme. The dynamic scheme makes use of priority handling and allows VP bandwidth to be shared among the VPs.Numerical results of the static and dynamic schemes are com-pared to evaluate their performance difference in terms of the total capacity and the total buffer required.