Kinetic aspects of adsorption determined by both bulk diffusion and surface activation barrier are analyzed theoretically for a spherical interface in contact with a finite volume of molecular or colloid solution. Rigorous transport equations for the bulk and surface phases are formulated together with general nonlinear boundary conditions which can be used for describing adsorption governed by various isotherms including those of Henry, Langmuir, Frumkin, etc. Explicit analytical results are derived by applying the Laplace transformation in the case of the ideal Henry isotherm for (i) a spherical adsorbing interface in contact with a quiescent solution of a finite or infinite extent and (ii) for a sphere surrounded by a stagnant layer of a finite thickness in contact with an infinite-sized reservoir of a well-stirred solution. Limiting short-time and long-time results as well as results derived in the special case of a plane geometry of the adsorbing surface are discussed. Using our general expressions the range of validity of equations previously known in the literature which were derived for the diffusion-controlled or surface barrier-controlled adsorption regime is estimated. In the general case of the nonlinear boundary conditions (Langmuir isotherm) an implicit numerical scheme is applied based on an “exact” solution of the set of nonlinear ordinary equations arising from the discretization of the surface kinetic equations.