A theory of phonon-assisted two-photon exciton transitions in indirect-band-gap semiconductor layered quantum wells (QW) and quantum well wires (QWW) is developed. The expressions for the two-photon absorption coefficients in one-dimensional (lD), a::', 2D, @, and 3D (bulk), a::), respectively, are calculated. The spectral dependence of these expressions, the vicinity of the band edge, are found to obey the law (2ho hS2 -E , + E&)O, where hw(hQ) is the photon (phonon) energy, E , the effective indirect gap, and Ek: the exciton binding energy. The values of /? vary from -f up to $ depending on the dimension of the system and the type of the coupling matrix element involved in each transition process. Before the edge, the final exciton states are of s-or p-symmetry according to the photon polarizations with respect to the confinement directions in the QWs and to the selection rules allowed by the momentum matrix elements. A numerical estimation for the case Si,.,Ge,,, shows that a::) for both photon polarizations (parallel and perpendicular to the confinement direction of the QWs) is enhanced over the values of u!:' and EL: ) (allowed and forbidden transitions). Furthermore ukl) is also enhanced over the u!:) values of bulk materials. This behaviour of the a,,' s is interpreted as due to (i) the additional confinement of the carriers which occur going from 3D + 2D -+ 1D systems, (ii) the photon polarization configurations with respect to the confinement directions, and (5) the coupling matrix elements.