While ray-optical methods have been employed for the analysis of high-frequency radiation and scattering problems and also for the study of optical resonators, their use for description of guided modes has been less evident. This paper presents a systematic procedure whereby the asymptotic functional dependences and eigenvalues of modes in uniform and nonuniform guiding structures are deduced by purely ray-optical means, utilizing either the eiconal and transport equations of geometrical optics or a modal consistency argument. The method is illustrated first on the simple example of a homogeneous plane slab, and is then applied to various nonuniform waveguides including an angular sector, a more general taper of either parabolic or hyperbolic shape, and a guide filled with an axially inhomogeneous dielectric. The role of caustics in the latter configurations is emphasized, and stress is placed throughout on a physical interpretation of relevant concepts which retain their validity even under conditions more general than those considered at present.