Abstract: In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H-weakly comodule coalgebras and Hmodule coalgebras．T he main result is to prove a structure theorem about B-cocleft H-module coalgebras．

Key words: H-module coalgebra, H-weakly comodule coalgebra, crossed coproduct