Attention is focused on nonlinear oscillations in the context of the singularly perturbed forced oscillator of Duffing’s type with a nonlinear restoring force
where are -functions on a given interval and is a -function on . The appearance of large frequency nonlinear oscillations of the solutions is explained. It is shown that the frequency can be controlled by a small parameter at the highest derivative. Analytical approximations to the double-well Duffing oscillator in large amplitude oscillations are derived. A new method for the analysis of nonlinear oscillations which is based on a dynamic change of coordinates is proposed.