Abstract: This paper deals with the random response of elastic-viscoelastic combined systems. A method is proposed on the basis of the complex analysis in the time domain, in which the differential and integral dynamic equation of an elastic-viscoelastic combined system is transformed into an ordinary state equation. The covariance matrices of random responses of elastic-viscoelastic systems under stationary random excitations are obtained. The characteristics of the systems under typical stationary random excitations are investigated and complex algebraic expressions of covariance matrices are given. It is shown that the present method is simple and widely applicable.