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The use of Java for parallel programming on clusters according to the message-passing paradigm is an attractive choice. In this case, the overall application performance will largely depend on the performance of the underlying Java message-passing library. This paper evaluates, models and compares the performance of MPI-like point-to-point and collective communication primitives from selected Java message-passing implementations on clusters with different interconnection networks. We have developed our own micro-benchmark suite to characterize the message-passing communication overhead and thus derive analytical latency models.