For an electron-phonon system with several equivalent bands a generalized transport and response theory is derived which serves as microscopic justification of a model for the structural phase transition in A15-compounds. By means of a generating functional approach a self-consistent formulation of the theory is achieved. The resulting set of coupled integral equations becomes closed within the ladder approximation. In particular, the functional formalism is used to calculate the generalized response occuring in a coupled electron-phonon system. In a subsequent paper a self-consistent solution of the coupled equation will be given with which the response functions are evaluated and discussed with recourse to the particularities of A15-compounds.
