a (b) It was shown /1/ that for the motion of Wannier-Mott excitons (in t e r m s of energy and momentum transfer), on can formulate the dynamical equations valid for the motion of a superfluid liquid /2, 3/. We have already demonstrated that this could be also done for Frenkel excitons /4/ and now we wish t o examine the influence of exciton-phonon interaction.W e shall consider the one-dimensional Hamiltonian which was formulated in /5/ (where the case of the Bose-Einstein condensation of Frenkel excitons a s well as the exciton drop formation was investigated) in the form (like in /6/)where A is the isolated molecule energy, X is the dipole-dipole interaction matrix element in the nearest neighbour approximation (X = -(X(