A frequency domain based algorithm using Fourier approximation and Galerkin error minimization has been used to obtain the periodic orbits of large order nonlinear dynamic systems. The stability of these periodic response is determined through a bifurcation analysis using Floquet theory. This technique is applicable to dynamic systems having both analytic and nonanalytic nonlinearities. This technique is compared with numerical time integration and is found to be much faster in predicting the steady state periodic response. © 2003 Elsevier Science Ltd. All rights reserved.