The zeolite-catalyzed dimerization of ethene, propene, I-butene, and trans-2-butene has been modeled using quantum chemical methods. Reactants, transition states, and products have been investigated. A cluster model consisting of four tetrahedrally coordinated atoms (T-atoms) has been used to represent the catalyst. Two different mechanism types have been evaluated: concerted and stepwise. In the concerted pathway, protonation and C-C bond formation occur simultaneously. The stepwise mechanism proceeds via alkoxide formation followed by C-C bond formation. The order of reactivity among the different alkene reactants has been assessed. Quantum chemistry predicts that the activation energy of the concerted mechanism lies between the two barriers of the stepwise mechanism. More detailed knowledge concerning the stability of alkoxide species relative to physisorbed alkenes will be necessary for discrimination between the two mechanistic proposals. Implications for the reverse reaction, the beta-scission of alkenes, are briefly discussed.