A heuristically-aided algorithm to achieve mutual exclusion in distributed systems is presented which has better performance characteristics than previously proposed algorithms. The algorithm makes use of state information, which is defined as the set of states of mutual exclusion processes in the system. Each site maintains information about the state of other sites and uses it to deduce a subset of sites likely to have the token. Consequently, the number of messages exchanged for a critical section invocation is a random variable between 0 and n (n is the number of sites in the system). It is shown that the algorithm achieves mutual exclusion and is free from deadlock and starvation. The effects of a site crash are discussed, as are those of a communication-medium failure on the proposed algorithm. Methods of recovery from these failures are suggested. The performance of the algorithm is studied using a simulation technique (and an analytic technique for low and heavy traffics of requests for critical section execution).< >