Context: Airglow emissions, such as previously observed from NO and O2(a-X) (0-0) on Venus, provide insight into the chemical and dynamical processes that control the composition and energy balance in the upper atmospheres of planets. The OH airglow emission has been observed previously only in the Earth's atmosphere where it has been used to infer atomic oxygen abundances. The O2(a-X) (0-1) airglow emission also has only been observed in the Earth's atmosphere, and neither laboratory nor theoretical studies have reached a consensus on its transition probability. Aims: We report measurements of night-side airglow emission in the atmosphere of Venus in the OH (2-0), OH (1-0), O2(a-X) (0-1), and O2(a-X) (0-0) bands. This is the first detection of the first three of these airglow emissions on another planet. These observations provide the most direct observational constraints to date on H, OH, and O3, key species in the chemistry of Venus' upper atmosphere. Methods: Airglow emission detected at wavelengths of 1.40-1.49 and 2.6-3.14 mum in limb observations by the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) on the Venus Express spacecraft is attributed to the OH (2-0) and (1-0) transitions, respectively, and compared to calculations from a photochemical model. Simultaneous limb observations of airglow emission in the O2(a-X) (0-0) and (0-1) bands at 1.27 and 1.58 mum, respectively, were used to derive the ratio of the transition probabilities for these bands. Results: The integrated emission rates for the OH (2-0) and (1-0) bands were measured to be 100 ± 40 and 880±90 kR respectively, both peaking at an altitude of 96 ± 2 km near midnight local time for the considered orbit. The measured ratio of the O2(a-X) (0-0) and (0-1) bands is 78 ± 8. Conclusions: Photochemical model calculations suggest the observed OH emission is produced primarily via the Bates-Nicolet mechanism, as on the Earth. The observed ratio of the intensities of the O2(a-X) (0-0) and (0-1) bands implies the ratio of their transition probabilities is 63±6.