Diffraction effects of a metallic cap located on a dielectric sphere on the propagation of high-frequency electromagnetic waves is investigated. The incident wave is supposed to be generated by a ring source located symmetrically with respect to the cap. Relying upon the locality principle of the GTD, the rigorous asymptotic solution is obtained by formulating the boundary-value problem in an abstract space in which the azimuth angle theta varies in the range theta is an element of (-infinity, infinity). The application of an integral transform with kernel Q(v-1/2)(-1)(cos theta), having similar analytical properties with Fourier integral transform, yields a scaler Hilbert problem which can be solved asymptotically for \kr\ much greater than 1 and then, edge and surface diffraction coefficients are obtained. (C) 1998 Elsevier science B.V. All rights reserved.