Laminar and turbulent one-dimensional lean premixed methane-air flames subject to equivalence ratio oscillations are investigated numerically. For the turbulent simulations, the Linear Eddy Model is employed. Harmonic perturbations at various frequencies and with various amplitudes are considered and their influence on CO and NO emissions, heat release rate fluctuations, and burning velocity is evaluated. The results indicate a strongly nonlinear behavior of the flame response for high forcing amplitudes attributed to nonlinear effects due to the interaction of burning velocity and equivalence ratio oscillations leading to nonsinusoidal oscillations at the flame front. Furthermore, the turbulent cases reveal decreasing mean burning velocities and heat release rates with increasing amplitudes due to damping of turbulent fluctuations induced by the oscillations.