It is shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin. At finite concentration localized excited states around classical spins form an "impurity band". The process of growth of the "impurity band" and its effects on observable quantities are investigated. § I. Introduction Since the monumental paper by Abrikosov and Gorkov 1 ) many works have been done experimentally and theoretically concerning the thermodynamic and transport properties of superconductors with small amount of paramagnetic impUrItIes. Recently several authors 2 ),3) have been interested in whe'ther loca­ lized excited states in the energy gap exist in a superconductor with a paramag­ netic impurity or not. As is well known, a paramagnetic impurity in a normal metal or a superconductor brings about the so-called Kondo effect 4 ) (a kind of quantum mechanical effects of spins) and this makes complete solutions of the problem quite difficult. In this paper we restrict our discussions to the classical spins in supercon­ ductors. In the s~d interaction between conduction electrons and a localized spin