A theory describing slow excitons which interact with longitudinal optical lattice vibrations is developed within the framework of the effective mass approximation. In many respects the theory is very similar to --and makes explicit use of --the ordinary theory of polarons which is used here in Gurari's formulation. Interesting differences with polaron theory are introduced by the fact that an exciton has an internal degree of freedom and is as a whole electrically neutral. Therefore the coupling to the lattice vibrations is less than that of a simple point charge and depends on the wave function of the internal motion and on the ratio of the effective masses of the two particles composing the exciton. In fact, the coupling is zero if these two masses are equal. As regards optical transitions of excitons to the ground state of the crystal it is demonstrated how the possibility for these transitions is determined by the properties of the wave function of the relative motion in combination with those of the Bloch functions of the valence-and the conduction band. Finally a general expression for the probality of such a transition with the simultaneous emission of some phonons is derived.