A new method of solution is presented for the analysis of unsteady e ows past oscillating airfoils. This method is based on the derivation of the singular contributions of the leading edge and ridges (points where the airfoil boundary conditions change ) in the solutions of the e uid velocity and pressure coefe cient. The method has been validated by comparison with the results obtained by Theodorsen and by Postel and Leppert for rigid airfoil and aileron oscillations in translation and rotation. An excellent agreement was found between the present solutions and these previous results. This method has then been used to obtain solutions for the e exural oscillations of the e exible airfoils, e tted or not with oscillating e exible ailerons, which are of interest for the aeroelastic studies. The aerodynamic stiffness, damping, and virtual (or added) mass contributions in the solutions of the unsteady pressure distribution, lift coefe cient, and moment coefe cient are specie cally determined. An analysis of the relative magnitude of the quasi-steady and vortex shedding contributions in the aerodynamic coefe cients is also presented. In all cases studied, this method led to very efe cient and simple analytical solutions in closed form.