The mechanisms of double-bond migration and the exchange of D2 with the hydrogen atoms of small cyclic olefins (methylenecyclobutane, methylenecyclopentane, cyclopentene, 3-methylcyclopentene, cyclohexene, and bicyclo-(2,2,1)-hepta-2, 5-diene) were investigated over a pure alumina catalyst. At temperatures below 100°, only those hydrogen atoms which were initially vinyl, or which could become vinyl by isomerization of the olefin, underwent exchange. A primary kinetic isotope effect of about 2.8 was found, indicating that cleavage of the C—H bond was probably the slow step in the exchange reaction. Rapid intermolecular scrambling of all vinyl hydrogen atoms was observed, and the presence of the olefins greatly reduced the usually fast rate of H2+ D2 equilibration. Double-bond migration below 100° was sensitive to the geometry of the olefin. Only molecules having a three carbon chain, including the double bond, which could appear concave when viewed from outside the molecule underwent isomerization; those which did not fulfill this requirement did not isomerize. Nearly pure 1,2-cyclopentene-d2 could be prepared, suggesting a dissociative mechanism for the exchange reaction. Hence, exchange and double-bond migration are independent processes, although both reactions may have involved the same sites and may have had a common intermediate. Poisoning experiments using radioactive CO2 indicated an active site density of about 1.4 × 1013 cm–2 for the exchange reaction after 530° pretreatment.