We investigate theoretically the possible manifestation of the small-polaron effect in the IR absorption spectrum of the one-dimensional molecular crystals. Phonon-induced relaxation of small-polarons is taken into account explicitly on the microscopic level. It was found that it may have substantial influence on optical properties of molecular crystals. Consequently, the accounting of the polaron relaxation effects on the microscopic level is necessary for proper understanding of the optical spectra of molecular crystals. Their hitherto interpretation in terms of polaron model, based on the phenomenological treatment of the polaron damping, has been critically assessed on the basis of our results. (C) 2009 Elsevier B.V. All rights reserved.