Using the generalized Gaussian distribution,this paper proposes an effective method to the analysis of the marginal and joint distributions of random responses of nonlinear structures subjected to random excitations. The marginal probability density function(PDF) of a nonlinear random response is modeled by the generalized Gaussian distribution and the joint PDF of the responses of interest is obtained by the Nataf model. The model parameters required by the method can be estimated by simple estimators. Numerical examples,a six-story shear-building structure under random earthquake loading,show that the method is very effective in the sense that it provides sufficiently exact solutions for the hardening as well as softening random responses with feasible computational efforts.