Dynamic program slicing methods are widely used for debugging, because many statements can be ignored in the process of localizing a bug. A dynamic program slice with respect to a variable contains only those statements that actually had an influence on this variable. However, during debugging we also need to identify those statements that actually did not affect the variable but could have affected it had they been evaluated differently. A relevant slice includes these potentially affecting statements as well, therefore it is appropriate for debugging. In this paper a forward algorithm is introduced for the computation of relevant slices of programs. The space requirement of this method does not depend on the number of different dynamic slices nor on the size of the execution history, hence it can be applied for real size applications.