Among all habitability factors for terrestrial exoplanets, one of the most important is the presence of a secondary N2–O2 dominant atmosphere in an exoplanet. This factor can potentially indicate the already existing geological and biological processes on the exoplanet. Meanwhile, direct characterization of the N2–O2 atmospheres of terrestrial exoplanets is a difficult observational task. There are only a few indicators (molecules) of such an atmosphere, among which one can single out a potential biomarker – a molecule of nitric oxide NO. The strongest spectral features of this molecule in the ultraviolet range are γ-bands (203–248 nm). An important role in the search for potential biomarkers on exoplanets, including the registration of NO γ‑bands, can be played by planned for the launch WSO-UV space observatory. In the paper estimates of the possibility of detecting the transmission of light in γ-bands in the atmospheres of exoplanets with this observatory are presented. The methods of emission and transmission spectroscopy are compared as applied to the detection of NO. Based on the results of this work, it is shown that there is a potential possibility of detecting a transmission signal in the NO γ-bands in the atmospheres of nearby exoplanets (10 pc) using the LSS spectrograph of the WSO-UV observatory. At the same time, the imposed restrictions for the registration of this signal on more distant exoplanets are presented.