Model Anderson-Holstein has been investigated previously by using diagrammatic approach for one impurity model and has been fo1mulated the main peculiarities of such complicated systems [ 1- 5]. Now we shall discuss the additional prope1iies of the two-impurity model conditioned by the presence of  the second center and the taken into account exchanges of quantum fluctuations between them. The Hamiltonian of this model has the fonn Here C.fo annihilation operators for conduction electrons, the faa such operators for impurity electrons and a operators for optical phonons. q and p coordinate and momentum of phonons: q = ._k (a+ a+ ) , p = F2, (a+ - a). Quantum index a = ± l dete1mine the spin of electron and a = 1, 2 dete1mine the two impurities. U0 is the Coulomb repulsion of the impurity electrons and 60 is local energy of these electrons, w0 - frequency of optical phonon. As in the case  of one impurity, we use the canonical transfonnation Lang-Firsov [ 6] of the Hamiltonian (1) This transfo1mation eliminates the  linear by phonon coordinate te1m of the Hamiltonian (2) and reno1malizes the Coulomb interaction. As a result of canonical transfonnation the additional attraction of impurity electrons appear of the 2 fonn ..!_  (L gana ) which contains besides the reno1malization of eve1y individual localized Coulomb  interaction also gives the additional collective reno1malization common for both impurity centers. The local pa.ii of our Hamiltonian has 16 self consisted functions which pe1mit us to obtain to express Fe1mi operators of  creation and annihilation of both impurity electrons with Hubbai·d This equation together with analogous equation for operator b; of the second impurity electron operator pennits us to dete1mine all dynainics quantities of local  subsystem, and fo1mulate the pe1iurbative theory for our strongly coITelated two impurity system.