In　this　paper,　we　investigate　the　two-stage　submodular　maximization　problem,　where　there　is　a　collection　F　=　{f(1,)　...,　f(m)}　of　m　submodular　functions　which　are　defined　on　the　same　element　ground　set　?.　The　goal　is　to　select　a　subset　S　subset　of　Omega　of　size　at　most　l　such　that　1/m　Sigma(f　is　an　element　of　F)maxT　subset　of　S,T　is　an　element　of　If(T)　is　maximized,　where　I　denotes　a　specificallydefined　independence　system.　We　consider　the　two-stage　submodular　maximization　with　a　P-matroid　constraint　and　present　a　(1/(　P　+　1))(1　-　1/e((P+1)))-approximation　algorithm.　Furthermore,　we　extend　the　algorithm　to　the　two-stage　submodular　maximization　with　a　more　generalized　P-exchange　system　constraint　and　show　the　approximation　ratio　can　be　maintained　with　slightly　modifications　of　the　algorithm.　(C)　2020　Elsevier　B.V.　All　rights　reserved.