The dynamic response of multiple-degree-of-freedom nonlinear structures is usually determined by numerical integration of the equations of motion, an approach which is computationally very expensive for steady-state response analysis of large structures. In this paper, an alternative semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations and the solution is obtained iteratively. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix [alpha], and the latter by the generalized quasilinear matrix [DELTA] which is updated at each iteration. A special technique that reduces the computation time significantly when the nonlinearities are localized is used with success to analyze large structures. The proposed method is fully compatible with standard modal analysis procedures. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented in the case of a ten-degree-of-freedom structure.