In “A theory of hypermodal logics: Mode shifting in modal logic” D.M.Gabbay founded a semantics of hypermodal logics based on any frame. He is the first one who founded a hypermodal logic si,. Well, Following Gabbay's paradigm, my thesis is to expand the semantics to transitive frames, based on which we are going to found a logic K4［T·，K·］.There, we are going to study the properties of two kinds of hypermodalities K4 and S4, espectially of the problem of nested hypermodalities.