The change in critical mass of a large reflector- moderated gaseous-fueled cavity reactor due to the presence of hot hydrogen gas in the cavity has been investigated using multithermal-group diffusion theory calculations that include up- and down- sea tiering between all groups. It is calculated, for example, that the critical mass of gaseous Pu-239 in the cavity is increased by more than a factor of 2 with the addition of hydrogen at 500 atm and 20,000 °K to a 137.25-cm-radius sperical cavity surrounded by a 91.5-cm thickness of beryllium oxide reflector-moderator. Critical masses of Pu-239 and of U-233 are presented for hydrogen pressures between 0 and 1500 atm, for hydrogen temperatures of 20,000° and 60,000 °K, for ratios of fuel radius to cavity radius of 1.0 to 0.45, and for two different reflector- moderator configurations. The thermal neutron flux distribution within the cavity is shifted by energy up- scattering collisions between thermal neutrons flowing into the cavity from the reflector-moderator and the hot hydrogen atoms. The relatively large thermal motion associated with hydrogen atoms at high temperatures gives rise to an increased probability for thermal neutron scattering, i.e., the scattering is a factor of 10 larger for a 2200 m/sec neutron in atomic hydrogen at 20,000 °K than at room temperature. The changes in critical masses may be accounted for largely by the changes in the flux-weighted fuel region cross sections, even for fuels having 1/t? cross-section dependences, since the radial neutron flux distribution and the neutron energy spectrum in the reflector- moderator are not strongly dependent upon cavity conditions. The average energy up-scattering increments for neutrons below 0.5 ev are about 1.5 and 5.2 ev for atomic hydrogen at 20,000° and 60,000°K, respectively. Thus, one scattering collision removes thermal neutrons from energy regions with high fission cross- section values up to regions with greatly reduced values. Critical mass increases are less drastic for U-233 than for Pu-239 because of the presence in U-233 of several fission resonances in the 1.0 to 10-ev energy range. The results of this study have been obtained using 18 neutron energy groups including 12 groups over the neutron energy range up to 3.06 ev. Calculated neutron flux spectra are presented to demonstrate the detailed nature of the calculational techniques and to show the changes in spectra which take place because of both hot hydrogen scattering and selective absorption of neutrons near the Pu-239 resonance at 0.3 ev.