The identification of linear structural dynamic systems has been dealt with extensively in past studies. Identification methods for nonlinear structures have also been introduced in previous articles, including procedures based on the method of multiple scales, iterative and noniterative direct methods, and state space mappings. Here, a procedure is introduced for the identification of nonlinear structural dynamic systems which is readily applicable to simple as well as more complex multiple degree of freedom systems. The procedure is based on multiple step integration methods for the solution of differential equations. The multiple step integration procedure and the iterative direct method are applied to a number of nonlinear single degree of freedom examples, and are applied to a simple two degrees of freedom example as well. RMS based noise is added to a simulated measured response in order to monitor the effects of measurement errors on the procedures. The input data is filtered before final processing in the identification algorithms. The multistep algorithm is compared to the iterative direct method on the basis of criteria such as accuracy, ease of use, and numerical efficiency. / Master of Science