A procedure to identify nonlinear structural systems caused by quadratic or cubic stiffness nonlinearity, geometric asymmetry, internal resonance, and subject to parametric excitation is proposed. The method uses conventional instrumentation and modal analysis techniques to match observed behavior in the structural response to the behavior of nonlinear analytical models when subject to random, impulse, or harmonic excitations. Some of the structures studied in this paper behave linearly when subject to one type of excitation but exhibit uniquely nonlinear behavior when subject to other types of excitation.