Super-Earth exoplanets are being discovered with increasing frequency and some will be able to retain stable H 2 -dominated atmospheres. We study biosignature gases on exoplanets with thin H 2 atmospheres and habitable surface temperatures, using a model atmosphere with photochemistry and a biomass estimate framework for evaluating the plausibility of a range of biosignature gas candidates. We find that photochemically produced H atoms are the most abundant reactive species in H 2 atmospheres. In atmospheres with high CO 2 levels, atomic O is the major destructive species for some molecules. In Sun-Earth-like UV radiation environments, H (and in some cases O) will rapidly destroy nearly all biosignature gases of interest. The lower UV fluxes from UV-quiet M stars would produce a lower concentration of H (or O) for the same scenario, enabling some biosignature gases to accumulate. The favorability of low-UV radiation environments to accumulate detectable biosignature gases in an H 2 atmosphere is closely analogous to the case of oxidized atmospheres, where photochemically produced OH is the major destructive species. Most potential biosignature gases, such as dimethylsulfide and CH 3 Cl, are therefore more favorable in low-UV, as compared with solar-like UV, environments. A few promising biosignature gas candidates, including NH 3 and N 2 O, are favorable even in solar-like UV environments, as these gases are destroyed directly by photolysis and not by H (or O). A more subtle finding is that most gases produced by life that are fully hydrogenated forms of an element, such as CH 4 and H 2 S, are not effective signs of life in an H 2 -rich atmosphere because the dominant atmospheric chemistry will generate such gases abiologically, through photochemistry or geochemistry. Suitable biosignature gases in H 2 -rich atmospheres for super-Earth exoplanets transiting M stars could potentially be detected in transmission spectra with the James Webb Space Telescope.