The Kerman-Klein-Dönau-Frauendorf (KKDF) model is a linearized version of the nonlinear 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 corresponding properties of neighboring even nuclei and of single-particle properties, which are the input parameters of the model. A divers sample of recent applications attests 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 with proton-neutron number (Z,N) that relates their properties to those of the four neighboring even-even nuclei (Z+1,N+1) , (Z-1,N+1) , (Z+1,N-1) , and (Z-1,N-1) , all of which are required 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 nucleus directly to those of the even-even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also resolve the problem of choosing the subspace of physical solutions that arises in an equation of motion approach that includes pairing interactions.