Sequence comparison is a basic operation in DNA sequencing projects, and most of sequence comparison methods used are based on heuristics, which are faster but there are no guarantees that the best alignments will be produced. On the other hand, the algorithm proposed by Smith-Waterman obtains the best local alignments at the expense of very high computing power and huge memory requirements. In this article, we present and evaluate our experiments with three strategies to run the Smith-Waterman algorithm in a cluster of workstations using a Distributed Shared Memory System. Our results on an eight-machine cluster presented very good speedups and indicate that impressive improvements can be achieved, depending on the strategy used. Also, we present some theoretical remarks on how to reduce the amount of memory used.