The time complexity of sorting n elements using p greater than equivalent to n processors on L. G. Valiant's (1975) parallel comparison tree model is considered. It is shown that this time complexity is THETA (log n/log(1 plus p/n)). For every fixed time k it is shown that OMEGA (n**1** plus **1 **/ **k ) comparisons are required and that there exists a randomized algorithm for comparison sort in time k with an expected number of O(n**1** plus **1 **k comparisons. This implies that for every fixed k, any deterministic comparison sort algorithm must be asymptotically worse than this randomized algorithm. It is shown that 'approximate sorting' in time 1 requires asymptotically more than n log n processors.