Two-photon absorption spectra (2PA) of a series of conjugated dimers and the corresponding monomer were studied in the near-IR region. All of the dimers show very large peak cross section values, sigma(2) = (3-10) x 10(3) GM (1 GM = 1 x 10(-50) cm(4) s photon(-1)), which is several hundred times larger than that obtained for the corresponding monomer in the same region. We explain such dramatic cooperative enhancement by a combination of several factors, such as strong enhancement of the lowest one-photon Q-transition, better resonance conditions in the three-level system, dramatic enhancement of the excited-state singlet-singlet transition, and parallel arrangement of consecutive transitions in dimers, as compared to perpendicular arrangement in the monomer. We show that the absolute values of the 2PA cross section in these molecules are quantitatively described by a quantum-mechanical expression, derived for the three-level model. We also demonstrate the possibility of singlet oxygen generation upon one- and two-photon excitation of these dimers, which makes them particularly attractive for photodynamic therapy.