An ab initio density-functional investigation of the physisorption and chemisorption of neutral and protonated n-olefins in the zeolitic 12-membered ring main channel of a zeolite has been performed for gmelinite. A linear increase of the energy of physisorption with the length of the hydrocarbon is observed in agreement with experimental data. Upon chemisorption, a covalent C(olefin)-to-O(zeolite) bond is formed producing a stable alkoxy species. The energy of chemisorption depends on both the zeolite O-site and the length of the olefin chain. Shorter molecules (ethene and,propene) chemisorbed at any of the crystallographically inequivalent O-sites on the inner surface of the zeolite (O1, O3, and O4) are more stable than physisorbed species. With the increasing length of the molecule the chemisorption energy decreases due to the deformation necessary to accommodate the molecule within the channel and due to the increasing repulsion between the molecule and the zeolite. The smallest deformation and repulsion is observed for the O4-site where chemisorbed molecules of any length are more stable than the physisorbed species. Better stabilization at the O4-site is achieved because of a more symmetric contact allowing the formation of the shortest and most stabilizing C-O bond. The chemisorption at the zeolite inner surface thus represents a possible reaction channel for the conversion of olefins in zeolites. Protonated molecules of short olefins (ethene, propene) collapse to neutral hydrocarbons. The cations formed by the protonation of butene and pentene are relatively stable in the zeolite disfavored by only similar to+70 kJ/mol as compared with chemisorbed species. Longer protonated molecules show increased stability with increasing chain length.