There is much experimental and mathematical work that describes chemical transport through multilayered films, which is relevant to transdermal drug delivery, for example. It is not directly applicable to chemical transport from multilayered materials with spherical geometries, however. These materials are of interest in biotechnological applications, such as drug delivery and immobilized biocatalysis. A general formulation is presented for the analytical solution of transient diffusion problems in multilayered spheres. The method is based on expansions in the orthogonal basis defined by eigenfunctions of self-adjoint, second-order Sturm-Liouville operators, according to the formalism of Ramkrishna and Amundson (1974). Scenarios involving diffusive release and a first-order chemical reaction in multilayered spherical structures are analyzed using this mathematical model.