Hydrogenolysis of propane and n-butane has been studied on highly dispersed Rh on SiO2, Al2O3 and TiO2 catalysts prepared by conventional impregnation, using thermal cycling between ca. 410 and 520 K. Rh/SiO2 is initially the most active for n-butane, but during thermal cycling it deactivates the fastest, with decrease in ethane selectivity S-2. Apparent activation energies are ca. 200 kJ mol(-1) for propane and ca. 190 kJ mol(-1) for n-butane. After the first high-temperature reduction (HTR1), values of S-2 in the n-butane reaction are between 1.1 and 1.6; they decrease significantly following oxidation and low-temperature reduction (O/LTR), but rise again after a second high-temperature reduction (HTR2). Dependence of rates of both reactions on H-2 pressure at ca. 430 K have been determined for each catalyst after HTR1, and also for Rh/TiO2 after O/LTR. Orders in H-2 are strongly negative; the results are modelled by a rate expression derived from a mechanism that assumes activation of the alkane by loss of several H atoms, and values of constants k(1) (rate constant), K-H (H-2 chemisorption) and K-C (alkane activation), are determined. K-H generally exceeds K-C, which on Rh/TiO2 is increased by O/LTR treatment. On Rh/SiO2, S-2 for the n-butane reaction is independent of H-2 pressure, but for the other systems it decreases as the H-2 pressure is raised. It is proposed that the chance of central C-C bond splitting in n-butane depends inter alia on the cleanliness of the Rh surface. Ethane selectivity in the propane reaction shows small dependence on either temperature or H, pressure for all systems, and is typically 0.98-0.99. The lack of a marked dependence of product selectivities on temperature and, except where noted, on H-2 pressure is attributed to the strong chemisorption of H-2 on these catalysts.