An investigation is made of the vibrational dephasing of a diatomic molecule absorbed on a surface. Explicit analytic forms for the rate of dephasing by phonons are derived. For comparison, an expression for energy relaxation is given which is appropriate for OH on SiO2. It is found that the dephasing rate is considerably faster for this system than the energy relaxation rate. These conclusions are compared with the results of a recent experiment. Keywords: Hydroxyl Radical/Silicon Dioxide System; Vibrational Dephasing; Energy Relaxation; Admolecules; Phonons; Quantum Mechanical.