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Unlike conventional packet switched networks, the ATM network is expected to perform connection-oriented operations for calls with variable traffic characteristics for each call. Fault tolerance in high speed ATM networks is greatly needed even for short-time link failures due to the large cell loss possibility. Here, we develop an ATM backbone network design algorithm by considering different Grades of Service (GOS) such as cell loss probabiliiy and mean end-to-end delay requirement for each call request. In addition, we ensure that these performance requirements are met even under faulty network conditions. Numerical examples show that our algorithm yields good solutions.