Dijkstra [1], Knuth [2], and de Bruijn [3] have discussed the problem of guaranteeing exclusive access to a shared resource in a system of cooperating sequential processes. The problem they deal with has been shown to have a relatively simple solution using the "P" and "V" operations of Dijkstra [4]. We discuss two related problems of practical significance in which we recognize two classes of processes wishing to use the resource. The processes of the first class, named writers, must have exclusive access as in the original problem, but processes of the second class, the readers, may share the resource with an unlimited number of other readers