  A model of alloy is considered which includes both quenched disorder in the
electron subsystem (``alloy'' subsystem) and electron-phonon interaction. For
given approximate solution for the alloy part of the problem, which is assumed
to be conserving in Baym's sense, we construct the generating functional and
derive the Eliashberg-type equations which are valid to the lowest order in the
adiabatic parameter.The renormalization of bare electron-phonon interaction
vertices by disorder is taken into account consistently with the approximation
for the alloy self-energy. For the case of exact configurational averaging the
same set of equations is established within the usual T-matrix approach. We
demonstrate that for any conserving approximation for the alloy part of the
self-energy the Anderson's theorem holds in the case of isotropic singlet
pairing provided disorder renormalizations of the electron-phonon interaction
vertices are neglected. Taking account of the disorder renormalization of the
electron-phonon interaction we analyze general equations qualitatively and
present the expressions for $T_{c}$ for the case of weak and intermediate
electron-phonon coupling. Disorder renormalizations of the logarithmic
corrections to the effective coupling, which arise when the effective
interaction kernel for the Cooper channel has the second energy scale, as well
as the renormalization of the dilute paramagnetic impurity suppression are
discussed.
