The　solution　to　a　generalized　longest　common　subsequence　problem　is　addressed　in　this　paper.　In　this　problem,　two　given　sequences　of　their　length　s　and　t　must　be　included　as　the　subsequences　of　the　two　main　sequences　A　and　B,　and　the　result　subsequences　must　be　the　longest.　If　the　lengths　of　the　two　main　sequences　A　and　B　are　n　and　m,　and　the　lengths　of　their　two　constrained　sequences　are　s　and　t　respectively,　the　time　complexity　of　the　dynamic　programming　algorithm　presented　in　this　paper　to　solve　the　new　generalized　LCS　problem　must　be　O(nmst).