A review of the solution techniques most widely used in nonlinear structural dynamics is presented. For nonlinear transient responses several explicit and implicit direct integration methods are compared with respect to accuracy, stability and computational efficiency. It is concluded that the choice of a suitable method depends upon the nature of the method, the formulation of finite element models, and the problem itself. In general, the Park method seems to be superior to the others in nonlinear dynamic analysis. If equilibrium iterations are performed at each time step, the Newmark— ß=1/4 method should be preferred.