The linear response of an oblique overdriven detonation to impose free stream disturbances or to periodic movements of the wedge is examined. The free stream disturbances are assumed to be steady vorticity waves and the wedge motions are considered to be time periodic oscillations either about a fixed pivot point or along the plane of symmetry of the wedge aligned with the incoming stream. The detonation is considered to be a region of infinitesmal thickness in which a finite amount of heat is released. The response to the imposed disturbances is a function of the Mach number of the incoming flow, the wedge angle, and the exothermocity of the reaction within the detonation. It is shown that as the degree of overdrive increases, the amplitude of the response increases significantly; furthermore, a fundamental difference in the dependence of the response on the parameters of the problem is found between the response to a free stream disturbance and to a disturbance emanating from the wedge surface.