With two-color picosecond infrared laser spectroscopy the dynamics of O-H and O-D stretch vibrations in zeolites are investigated. Zeolites appear to be good model systems to study transfer of vibrational energy in a solid. For the O-D vibrations, transient spectral holes are burnt in the inhomogeneously broadened absorption bands by saturating the absorption with a strong pump pulse. From the spectral hole widths the homogeneous absorption linewidths are obtained. The excited population lifetimes are determined using a time-resolved pump-probe technique, and in combination with the homogeneous linewidth the pure dephasing time is revealed as well. For high concentrations of O-H oscillators the vibrational stretch excitations are found to diffuse spectrally through the inhomogeneous absorption band. This spectral diffusion process is explained by direct site-to-site transfer of the excitations due to dipole-dipole coupling (Förster transfer). The dependences of the transient spectral signals on oscillator concentration and the results of one-color polarization resolved experiments confirm this explanation. The spectral transients are satisfactorily described by simulations in which the site-to-site transfer by dipole-dipole coupling is taken into account.