In this paper we study the global optimality conditions for some nonconvex quadratic program problems with quadratic constraints by using a new approach to establish sufficient global conditions suggested by Z. Y. Wu recently, and obtain some sufficient global optimality conditions for some nonconvex quadratic programs with quadratic constraints and derive some sufficient global optimality conditions of some nonconvex unconstrained quadratic programs at the same time. We also prove that in some special cases some results obtained in this paper are equivalent to the results in some references and even extend some corresponding results in some references in present information.