In recent years, emerging applications introduced new constraints for data mining methods. These constraints are typical of a new kind of data: the data streams. In data stream processing, memory usage is restricted, new elements are generated continuously and have to be considered in a linear time, no blocking operator can be performed and the data can be examined only once. At this time, only a few methods has been proposed for mining sequential patterns in data streams. We argue that the main reason is the combinatory phenomenon related to sequential pattern mining. In this paper, we propose an algorithm based on sequences alignment for mining approximate sequential patterns in Web usage data streams. To meet the constraint of one scan, a greedy clustering algorithm associated to an alignment method is proposed. We will show that our proposal is able to extract relevant sequences with very low thresholds.