Substitution of a H atom by an alkyl group on the terminal carbon of the alkyne moiety of 1,6-fullerenynes has a strong impact on the products of the reaction undergone by this species after thermal treatment. While the reaction of 1,6-fullerenynes bearing an unsubstituted alkyne moiety results in the cycloaddition of the alkyne group to the fullerene double bond leading to cyclobutene-fused derivatives, the presence of an alkyl substituent leads to the formation of allenes. In the present work, we have performed an exhaustive theoretical analysis of all possible reaction mechanisms leading to cyclobutene-fused derivatives and allenes to offer an explanation of the reactivity differences observed. The results obtained show that formation of cyclobutene-fused derivatives occurs through a stepwise diradical reaction mechanism, while allene formation proceeds through a concerted way involving an uncommon intramolecular ene process. For the 1,6-fullerenynes bearing a substituted alkyne, the ene reaction path leading to allenes has an energy barrier somewhat lower than the stepwise diradical mechanism for the cyclobutene-fused derivative formation, thus explaining the outcome of the reaction.