In this paper,by using the generalized It formula,a generalized existence-and-uniqueness theorem for hybrid stochastic differential delay equations(SDDEs) is established under the local Lipschitz condition and the generalized Khasminskii-type conditions.The generalized Khasminskii-type theorem covers a wide class of nonlinear hybrid SDDEs.Finally,an example is given to illustrate the application of the theory.