By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author,some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces.As applications,some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces.These theorems unify,improve and generalize some important known results in literature.