The polyhedral cage volumes of structure I (sI) (carbon dioxide, methane, trimethylene oxide) and structure II (sII) (methane-ethane, propane, tetrahydrofuran, trimethylene oxide) hydrates are computed from atomic positions determined from neutron powder-diffraction data. The ideal structural formulas for sI and sII are, respectively, S2L6 ?? 46H2O and S16L???8 ?? 136H2O, where S denotes a polyhedral cage with 20 vertices, L a 24-cage, and L??? a 28-cage. The space-filling polyhedral cages are defined by the oxygen atoms of the hydrogen-bonded network of water molecules. Collectively, the mean cage volume ratio is 1.91 : 1.43 : 1 for the 28-cage : 24-cage : 20-cage, which correspond to equivalent sphere radii of 4.18, 3.79, and 3.37 A??, respectively. At 100 K, mean polyhedral volumes are 303.8, 227.8, and 158.8 A??3 for the 28-cage, 24-cage, and 20-cage, respectively. In general, the 20-cage volume for a sII is larger than that of a sI, although trimethylene oxide is an exception. The temperature dependence of the cage volumes reveals differences between apparently similar cages with similar occupants. In the case of trimethylene oxide hydrate, which forms both sI and sII, the 20-cages common to both structures contract quite differently. From 220 K, the sII 20-cage exhibits a smooth monotonic reduction in size, whereas the sI 20-cage initially expands upon cooling to 160 K, then contracts more rapidly to 10 K, and overall the sI 20-cage is larger than the sII 20-cage. The volumes of the large cages in both structures contract monotonically with decreasing temperature. These differences reflect reoriented motion of the trimethyelene oxide molecule in the 24-cage of sI, consistent with previous spectroscopic and calorimetric studies. For the 20-cages in methane hydrate (sI) and a mixed methane-ethane hydrate (sII), both containing methane as the guest molecule, the temperature dependence of the 20-cage volume in sII is much less than that in sI, but sII is overall larger in volume.