One of the important parameters in the analysis and design of large space structures is to account for the dynamic forces induced by wind and the subsequent progressive collapse. During the past two decades, problems of extreme loading conditions have been considered by some authors, and special attention has been devoted to the collapse modes. Nonlinear time history dynamic analysis, involving the post-buckling characteristics of the space structures, may be analyzed using the conventional finite element method. However, to guarantee stability and accuracy of the solution, the number of elements used to model the structure may be very large. In this respect, the nonlinear spectral element method (SEM) is developed for analyzing dynamic problems in large space structures. Through use of a computer program, the proposed method has been used to obtain the nonlinear dynamic response of guyed power transmission towers under severe wind loading condition. Key words: nonlinear dynamic analysis, space structures, guyed towers, spectral element method.