Clusters of symmetric multiprocessors (SMPs) have emerged as the primary candidates for large scale multiprocessor systems. In this paper, we introduce an efficient sorting algorithm for clusters of SMPs. This algorithm relies on a novel scheme for stably sorting on a single SMP coupled with balanced regular communication on the cluster. Our SMP algorithm seems to be asymptotically faster than any of the published algorithms we are aware of. The algorithms were implemented in C using Posix Threads and the SIMPLE library of communication primitives and run on a cluster of DEC AlphaServer 2100A systems. Our experimental results verify the scalability and efficiency of our proposed solution and illustrate the importance of considering both memory hierarchy and the overhead of shifting to multiple nodes. (Also cross-reference as UMIACS-TR-97-69