In structural engineering, it is common to neglect the nonlinear effects. This is no longer feasible with increasing complex designs and higher demands on the simulation models. This thesis presents a study of the concept of nonlinearity in a structure with emphasis on system identification. Two identification methods are presented in this work. The first method uses a least-square technique in time domain and the second method uses a least-square technique in the frequency domain. These two methods are compared with each other for two different types of excitation: transient and random excitation. The study involves three stages; theoretical modeling, simulation and experimental verification. A single degree of freedom system is used for the simulations and a beam with a local nonlinearity is used in the experiment. The result shows that both identification methods work on simulated data, whereas only the frequency domain method worked well on experimental data. The transient excitation was better on simulated data compared to random excitation, however in the experiment the random excitation gives a more stable and reasonable result.