A lifting-surface theory of oscillating high-speed propellers has already been formulated by the author in a form of integral equations. The purpose of this note is to propose a method for solution of these integral equations. An adjoint variational principle, equivalent to the integral equations for direct and reverse flows as well as to the Kutta conditions in both the flows, is derived. It is shown that the generalized aerodynamic forces acting on the propeller blades will be computed advantageously by applying a Rayleigh-Ritz type method to the variational principle.