Transient behavior of desorption from a fixed-bed packed with thin-film-coated monodisperse spherical particles/hollow spheres by a flowing medium where the coated layer/spherical shell wall contains the desorbed component is modeled. The governing equations are solved analytically and breakthrough curves are determined for the system's parameters by numerical integration of the obtained infinite integral. The results are extended to similar kinetics of a fixed-bed system for solid diffusion into spherical particles. A closed form asymptotic solution for fixed-bed desorbers with monodisperse spherical particles is obtained, and the results are generalized for sorption (adsorption/desorption) systems.