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A complete mechanism for tolerating multiple failures in parallel computer systems, denoted as Immunet, is described in this paper. Immunet can be applied to arbitrary topologies, either regular or irregular, exhibiting in both cases graceful performance degradation. Provided that the network remains connected, Immunet is able to deal with any number of failures regardless of their spatial and temporal distribution. Our mechanism operates on the basis of a dynamic network reconfiguration in response to failures. The network reconfiguration only employs local information recorded at the router nodes which leads to a highly scalable system. In addition, its low cost and overhead permit a practicable hardware implementation. Finaly, Immunet could allow circumvent failures transparently to applications running on a parallel system because it does not require dropping in-flight traffic. Only packets stored in or traveling through a broken component should be recovered by higher system levels.