The authors study the power of shared-memory in models of parallel computation. They describe a novel distributed data structure that eliminates the need for shared memory without significantly increasing the run time of the parallel computation. More specifically they show how a complete network of processors can deterministicly simulate one PRAM step in O(log n(log log n)**2 ) time, when both models use n processors and the size of the PRAM's shared memory is polynomial in n. (The best previously known upper bound was the trivial O(n)). They also establish that this upper bound is nearly optimal. They prove that an online simulation of T PRAM steps by a complete network of processors requires OMEGA (T(log n)/(log log n)) time. A simple consequence of the upper bound is that an Ultracomputer (the only currently feasible general-purpose parallel machine) can simulate one step of a PRAM (the most convenient parallel model to program) in O((log n log log n)**2 ) steps.