The nonlinear autoregressive moving average model with exogenous inputs (NARMAX model) is a convenient digital representation that can be used to simulate a large class of nonlinear vibratory systems. However, the process of identifying the model structure and estimating the model term coefficients can be prohibitively computationally intensive. Most identification techniques start with a model structure containing all possible terms and then use an algorithm to determine the significance of each term and reduce the model size by eliminating insignificant terms. For many physical systems of interest (such as those with high order dynamics or multi-inputs/multi-outputs), the size of the model can exceed the available computational resources. It therefore becomes necessary to apply all available knowledge of the physical system to eliminate terms from the initial model structure and reduce this task to manageable proportions. To explore the utility of this identification method, it was used to identify the NARMAX model for a numerically generated single degree of freedom system. The identified model was used to simulate the system; a comparison is made between the numerically integrated response and the NARMAX simulated response. However, it is one thing to test system identification techniques by applying them to numerically generated data and quite another to use data which has been measured from a physical system. Not only are there differences between the ideal model of the system and the physical system, the measurement process introduces other changes to the data such as sampling effects, quantization effects, filtering effects, and measurement induced noise. In order to determine what effects on the model identification process are introduced by each step in the measurement process, the numerically integrated data was successively modified to simulate the effects of filtering and quantization (which introduces measurement noise) and the model identification process was performed on this altered data. These newly identified models were again used to simulate the system for purposes of comparison. Finally, the model identification process is applied to data measured from a physical system and the resulting model is evaluated for the purpose of simulation.