  The periodic s-d(f) exchange model is characterized by a wide variety of
interesting applications, a simple mathematical structure and a limited number
of reliable approximations which take care of the quantum nature of the
participating spins. We suggest the use of a projection-operator method for
getting information perturbationally, which are not accessible via diagrammatic
approaches. In this paper we present in particular results beyond perturbation
theory, which are obtained such that almost all exactly known limiting cases
are incorporated correctly. We discuss a variety of possible methods and
evaluate their consequences for one-particle properties. These considerations
serve as a guideline for a more effective approach to the model.
