Perturbations to the OH and OI [O(1S) 557.7 nm] airglow layers by ducted gravity waves near the Brunt-Väisälä period are investigated using a 2-D numerical model. Airglow signatures of these waves are strongly determined by perturbations of O, O3, and H, which exhibit peak densities near and above mesopause. Strong periodic vertical wind components of short-period gravity waves induce opposite relative density perturbations above and below the layer density peaks. Airglow signatures for ducted waves depend on the specific vertical shapes and altitudes of the wave packets relative to ambient species density profiles; waves perturbing only the bottoms or tops of the layers produce signatures differing from those able to perturb the entire layer thickness. Line-of-sight cancellation occurs between opposite perturbations above and below airglow layer peaks, even for standing waves without vertical phase progression. Integrated brightness-weighted temperature and intensity can thus appear in-phase or antiphase for standing waves, depending on the wave-packet altitude relative to the density gradients. Comparisons of OH and OI layer intensities also reveal in-phase or antiphase relative intensity responses and do not directly indicate the phase of the wave perturbations at layer peak altitudes. Despite this ambiguity, simultaneous brightness-weighted temperature measurements may provide additional insight into wave structure, amplitude, and trapping altitude. For waves of sufficient amplitude that perturb steep density gradients, nonlinearity of the airglow response may be observable; this effect is most prominent when strong cancellation of the linear signature occurs.