A one-dimensional model is used to investigate the relations between gravity waves and O2 and OH airglows perturbations. The amplitude and phase of the airglow perturbations induced by gravity waves (with period > 20 min) are calculated for different vertical wavelength (10--50 km) and damping rate. The model shows that for vertically propagating gravity waves, the amplitude of airglow perturbations observed from ground is larger for longer vertical wavelength, because of the smaller cancellation effect within each layer. The ratio of the amplitudes between O2 and OH is smaller for larger wave damping. For upward propagating (downward phase progression) waves, the intensity perturbation in O2 leads OH, and their phase difference (O2 minus OH) is larger for smaller vertical length and/or stronger damping. The rotational temperature perturbation leads intensity perturbation in both layers. Their phase difference is also larger for smaller vertical length but is smaller for stronger damping. Based on these relations, the vertical wavelength and damping rate of gravity waves can be derived from simultaneous measurements of airglow perturbations in O2 and OH layers.