We calculated the response of gas-cavity dosimeters to 25- and 45-MeV neutrons in order to estimate the portion of the response that originates from neutron interactions within the gas cavity. This affords insight into the validity of the Bragg-Gray theory for dosimeters with finite cavities and also provides a basis for modifying gas-to-wall absorbed dose conversion factors deduced from the Bragg-Gray theory for use with small-cavity dosimeters. For a typical ionization chamber, e.g., with a 1-cm3 propane-based tissue-equivalent gas at standard temperature and pressure, the fraction of the total absorbed dose to the gas cavity from neutron interactions within the gas is 0.09% at 25-MeV and 0.006% at 45-MeV neutron energies. For microdosimetric detectors, the neutron interactions within the gas are negligible above 25 MeV.