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Under weaker conditions on the kel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions (with symbols which are BMO functions and their weighted version,respectively) on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley g-functions.