The first parallel sort algorithm for shared memory MIMD (multiple-instruction-multiple-data-stream) multiprocessors that has a theoretical and measured speedup near linear is exhibited. It is based on a novel asynchronous parallel merge that evenly partitions data to be merged among any number of processors. A benchmark sorting algorithm is proposed that uses this merge to remove the linear time bottleneck inherent in previous multiprocessors sorts. This sort, when applied to data set on p processors, has a time complexity of O((n log n)/p)+O((n log p)/p) and a space complexity of 2n, where n is the number of keys being sorted. Evaluations of the merge and benchmark sort algorithms on a 12-processor Sequent Balance 21000 System demonstrate near-linear speedup when compared to sequential Quicksort.>