The saturation kinetics of the H-bond absorption spectra in a strong laser field is described as a level-crossing problem with diffusional motion along the reaction coordinate. The full analogy with kinetics and rate of electron transfer reactions is emphasized when vibrational relaxation to the ground state is negligible. In this case, the transition rate saturates with a field strength reaching the diffusional regime limited by the friction in the ground or excited state. Taking vibrational relaxation into consideration changes qualitatively the kinetics of approaching the stationary level populations and absorption of pumping light. The fast relaxation results in significant desaturation of the light induced transitions and a shortening of the transient time. The absorption spectra of the weak probe light in the context of two-level and three-level models show either loss or gain in the red wing, as well as bleaching and superabsorption in the corresponding transmission spectra. The time evolution of these spectra, after switching the strong field on and off, was studied.