The rate of detrapping of atomic hydrogen from several octasilsesquioxanes is the same for dissolved and solid samples and is independent of the presence of other species such as free radicals or oxygen; varying the cage substituents leads to only minor differences in the activation parameters. Hydrogen atoms are found to be more strongly stabilized in homosubstituted octasilsesquioxanes compared with singly Ge-substituted cages. A kinetic isotope effect observed for the detrapping of H and D from MeT8 is ascribed to the difference in the zero-point energies of the trapped atoms. There is a secondary H/D isotope effect in the temperature dependence of the Si-29-superhyperfine splitting constants in the range 228-353 K. Cage relaxation has a substantial effect on the detrapping barrier but little influence on the intracage potential. Calculations using a rigid cage approximation give satisfactory agreement with zero-point parameters extracted from experimental data. Different model chemistries yield qualitatively different pictures of the dependence of the hyperfine coupling constant of the trapped H atom upon the detrapping coordinate. Within an isotropic approximation of the vibrational displacements, the B3LYP data give fairly close agreement with the experimental temperature dependence, subject to a shift of the absolute value related to known weaknesses of the method. For the Si7Ge cage, it is found that the transition state in which the H atom passes through a Ge-containing face is strongly favored, accounting for the larger detrapping rate parameters observed experimentally for this species.