Measurements of self-excited combustion instability were performed in a lean-premixed, swirl-stabilized, gas turbine combustor in order to characterize the interaction between the fundamental and higher harmonics of dynamic pressure, heat release rate, and acoustic velocity perturbations. The formation of higher harmonics, their interactions with the fundamental, and the influence of these interactions on nonlinear combustion processes are highlighted in this article. A detailed analysis of the fundamental and higher harmonics of the pressure signal reveals that for a small amplitude disturbance the second harmonic of the pressure signal is governed by a quadratic function. For high amplitude disturbances, the measured data deviate from the power law dependence; this is a manifestation of nonlinear energy transfer toward higher harmonic components. The disturbance amplitude at which the inception of the non-quadratic dependence occurs coincides with the transition from linear to nonlinear heat release response. In particular, the higher harmonic characteristics are significantly altered by varying swirler location, which is known as a primary source of vortical disturbance in swirl-stabilized combustion systems. As a result, for certain inlet conditions, the amplitude of the higher harmonic of acoustic velocity is even higher than the amplitude of the fundamental, and this leads to multiple-frequency excitation. The system then evolves toward a periodic state that is completely different from that of a system with single frequency excitation.