In this paper we consider the problem of the incremental mining of sequential patterns when new transactions or new customers are added to an original database. We present a new algorithm for mining frequent sequences that uses information collected during an earlier mining process to cut down the cost of finding new sequential patterns in the updated database. Our test shows that the algorithm performs significantly faster than the naive approach of mining on the whole updated database from scratch. The difference is so pronounced that this algorithm could also be useful for mining sequential patterns, since in many cases it is faster to apply our algorithm than to mine sequential patterns using a standard algorithm, by breaking down the database into an original database plus an increment. Key words: Sequential patterns, incremental mining, data mining