The need to search for complex and recurring patterns in database sequences is shared by many applications. In this paper, we discuss how to express and support efficiently sophisticated sequential pattern queries in databases. Thus, we first introduce SQL-TS, an extension of SQL, to express these patterns, and then we study how to optimize search queries for this language. We take the optimal text search algorithm of Knuth, Morris and Pratt, and generalize it to handle complex queries on sequences. Our algorithm exploits the inter-dependencies between the elements of a sequential pattern to minimize repeated passes over the same data. Experimental results on typical sequence queries, such as double bottom queries, confirm that substantial speedups are achieved by our new optimization techniques.