This paper considers small periodic perturbations of second order nonlinear Duffing type equations. It is concerned with the phenomenon known as ``period doubling bifurcation'' interpreted as the combination of two unperturbed equation, whose periods are close to the period of the perturbation. This phenomenon is contrasted to the subharmonic bifurcation. A sort of bifurcation equation is derived, using the above interpretation. Duffing equation with a specific perturbation term serves as an example. The paper ends up with a brief discussion, on the grounds of numerical computations.