The vibrational relaxation and the diffusion of diatomic molecules in the zeolite silicalite have been studied through molecular dynamics simulations in the microcanonical statistical ensemble. The adopted model accounts for the vibrations of the framework and sorbed atoms using a harmonic potential for the silicalite and a Morse potential for the diatomic molecule. The results show that the framework favors the relaxation of diatomics oscillating at frequencies near to its characteristic vibrational frequencies, leading in such cases to lower relaxation times and to an increasing in the energy exchanged per collision. The diffusion of a two-site oscillating molecule representing ethane has been also investigated; the diffusion coefficient and the heat of adsorption agree very well with the experimental data. Arrhenius parameters for the diffusion have been calculated, and some insights into the diffusion mechanism have been obtained from log-log plots and by inspection of the distribution of the ethane molecules in the silicalite channels. Therefore the simplified model adopted seems to adequately describe the diffusive motion and the guest-host energy exchanges, and it could be useful in order to study simple bimolecular reactions in zeolites.