In　this　paper,　we　consider　a　generalized　longest　common　subsequence　problem,　in　which　a　constraining　sequence　of　length　s　must　be　included　as　a　substring　and　the　other　constraining　sequence　of　length　t　must　be　included　as　a　subsequence　of　two　main　sequences　and　the　length　of　the　result　must　be　maximal.　For　the　two　input　sequences　X　and　Y　of　lengths　n　and　m,　and　the　given　two　constraining　sequences　of　length　s　and　t,　we　present　an　O(nmst)　time　dynamic　programming　algorithm　for　solving　the　new　generalized　longest　common　subsequence　problem.　The　time　complexity　can　be　reduced　further　to　cubic　time　in　a　more　detailed　analysis.　The　correctness　of　the　new　algorithm　is　proved.　©　Springer　International　Publishing　Switzerland　2016.