The transversal hypergraph enumeration based algorithms can be efficient in mining frequent itemsets, however it is difficult to apply them to sequence mining problems. In this paper we first analyze the constraints of using transversal hypergraph enumeration in itemset mining, then propose the ordered pattern model for representing and mining sequences with respect to these constraints. We show that the problem of mining sequential patterns can be transformed to the problem of mining frequent ordered patterns, and therefore we propose an application of the Dualize and Advance algorithm, which is transversal hypergraph enumeration based, in mining sequential patterns.