This thesis describes an experimental investigation of the flame transfer function between flow disturbances and heat release oscillations in lean, premixed combustors. This research effort was motivated by the fact that modern gas turbines, operating fuel-lean to minimize exhaust emissions, are susceptible to self-excited combustion oscillations. These instabilities generally occur when the unsteady combustion process couples with the acoustic modes of the combustion chamber. The resultant flow and structural vibrations can substantially reduce hot section part life. As such, avoiding operating regimes where high dynamics occur often requires operating at lower power outputs and/or higher pollutant emissions than the turbine is otherwise capable. This work demonstrated nonlinearities in the chemiluminescence response at large amplitude velocity oscillations in a turbulent, swirling flame. It is observed that the nonlinear flame response can exhibit a variety of behaviors, both in the shape of the response curve and the forcing amplitude at which nonlinearity is first observed depending on the operating conditions of the combustor. The phase between the flow oscillations and heat release is also seen to have substantial amplitude dependence. In addition, the interactions between the fundamental frequency and the higher and subharmonics of the measured signals can significantly influence the flame as well as the frequency response of the system. The nonlinear flame dynamics are governed by different mechanisms in different frequency and flowrate regimes. Three mechanisms, vortex rollup, unsteady flame liftoff, and parametric instability, are identified to influence the nonlinear flame response in these combustors. Analysis of the results shows that the mechanisms responsible for nonlinearity in the flame response are influenced by the Strouhal number, the mean velocity at the combustor dump plane, and the ratio of the oscillating velocity amplitude to the laminar flame speed.