  The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the
Kerman-Klein (equations of motion) formulation of the nuclear many-body
problem. In practice, it is a generalization of the standard core-particle
coupling model that, like the latter, provides a description of the
spectroscopy of odd nuclei in terms of the properties of neighboring even
nuclei and of single-particle properties, that are the input parameters of the
model. A divers sample of recent applications attest to the usefulness of the
model. In this paper, we first present a concise general review of the
fundamental equations and properties of the KKDF model. We then derive a
corresponding formalism for odd-odd nuclei that relates their properties to
those of four neighboring even nuclei, all of which enter if one is to include
both multipole and pairing forces. We treat these equations in two ways. In the
first we make essential use of the solutions of the neighboring odd nucleus
problem, as obtained by the KKDF method. In the second, we relate the
properties of the odd-odd nuclei directly to those of the even nuclei. For both
choices, we derive equations of motion, normalization conditions, and an
expression for transition amplitudes. We also solve the problem of choosing the
subspace of physical solutions that arises in an equations of motion approach
that includes pairing interactions.
