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This paper studies Morita duality of semigroup-graded rings,and discusses an equivalence between duality functors of graded module category and bigraded himodules.An important result is obtained:A semigroup bigraded R-A-bimodule Q defines a semigroup graded Morita duality if and only if Q is gr-faithfully balanced and Ref(RQ),Ref(QA) is closed under graded submodules and graded quotients.