At low conversion, isomerization of methylcyclopentane (MCP) to cyclohexane (CH) at 65 degrees C is faster on sulfated zirconia (SZ) than on AlCl3 containing traces of water, but the latter reaction reaches equilibrium much quicker because the former deactivates rapidly. Dimer formation (C12H22) occurs On SZ faster in the early stages and continues throughout the reaction, whereas AlCl3 forms essentially no dimers at first, but in late stages of reactions, when a "sludge" is expected to be formed on AlCl3, some dimers are observed, but always much less than on SZ. This difference was predicted, because on SZ the dimers are formed by two pathways, dimerization of free radicals formed in the oxidative initiation step and alkene alkylation by carbocations later on, whereas only the latter mechanism is available for AlCl3. Pretreatment with SO2, which is a good solvent for carbocations, increases substantially the activity of AlCl3 (which retains up to 30% SO2) most likely by generation of a liquid film which contains carbocations in solution. By contrast, SZ is completely deactivated by this treatment, possibly from a combination of traces of water and loss of oxidizing ability. Dimer formation on AlCl3 increases appreciably after pretreatment with SO2, as expected for the reaction in a liquid film where a higher concentration of carbocations facilitates bimolecular reaction. Dimer formation on SZ is much reduced, but not entirely suppressed by pretreatment with SO2 and the distribution of isomers is different for the two catalysts after pretreatment, showing that some oxidizing ability is retained by SZ, even though the further conversion of hydrocarbon is inhibited. All these results provide further support for the bifunctional nature (initiation by one-electron oxidation followed by acid-catalyzed, carbocationic, reaction of intermediates like surface esters and alkenes formed in the first step) advanced earlier by the authors for the sulfated metal oxides.