A new parallel sorting algorithm, called parsort, suitable for implementation on tightly coupled multiprocessors is presented. The algorithm is based upon quicksort and two‐way merging. An asynchronous parallel partitioning algorithm is used to distribute work evenly during merging to ensure a good load balance amongst processors, which is crucial if we are to achieve high efficiency. The implementation of this parallel sorting algorithm exhibits theoretical and measured near linear speed‐up when compared to sequential quicksort. This is illustrated by the results of experiments carried out on the Sequent Balance 8000 multiprocessor.