The method of integral equations and representation of unknown surface currents as a sum of ''uniform'' and ''nonuniform'' components are used to solve a very large class of diffraction problems, such as dielectric, multilayered, partially coated, and other objects, including the structures with surface waves. They can be used as canonical problems to considerably extend the field of application of the geometrical and physical theories of diffraction. A simple example (diffraction by a dielectric slab of finite width) is considered in order to illustrate the implementation and validity of our hybrid approach where the possibilities of both numerical and asymptotic methods are combined. The diffraction of the second order is taken into account. It is shown by comparison with the direct numerical calculations that the contribution of the third- and higher-order diffraction is too small and practically may be neglected. ¿ American Geophysical Union 1996