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Sequential pattern mining is an active field in the domain of knowledge discovery. Recently, with the constant progress in hardware technologies, real-world databases tend to grow larger and the hypothesis that a database can be loaded into main-memory for sequential pattern mining purpose is no longer valid. Furthermore, the new model of data as a continuous and potentially infinite flow, known as data stream model, call for a pre-processing step to ease the mining operations. Since the database size is the most influential factor for mining algorithms we examine the use of sampling over static databases to get approximate mining results with an upper bound on the error rate. Moreover, we extend these sampling analysis and present an algorithm based on reservoir sampling to cope with sequential pattern mining over data streams. We demonstrate with empirical results that our sampling methods are efficient and that sequence mining remains accurate over static databases and data streams.