Saturation of the H-bond absorption spectra by a strong laser field is described as a level-crossing problem with diffusional motion along the reaction coordinate. The stationary populations of the ground and excited vibronic states were found, assuming that the light induced transitions between them occur only at the point of exact resonance and the nonradiative decay of the upper state is uniform. The stationary distributions in both states are also obtained and shown to be Gaussian at slow vibrational relaxation, but essentially distorted when relaxation is faster than diffusion. The absorption spectra of the weak probe light in the frame of two-level and three-level models are calculated, which show either loss or gain in different spectral regions. The existence of bleaching and superabsorption branches in corresponding transmission spectra are confirmed.