Ab inito predictions of the proton-transfer reaction rates in chabazite, faujasite, and ZSM-5 zeolites are presented. The reaction studied, a proton jump between neighboring oxygen atoms of the AlO4 tetrahedron, defines proton mobility in an unloaded catalyst. Classical transition state theory is applied, and the potential energy surface is described by the QM-Pot method. The latter combines a quantum mechanical description of the reaction site with an interatomic potential function description of the periodic zeolite lattice. At room temperature, the calculated rates vary over a broad range of 10(-6) to 10(5) s(-1), depending on the zeolite type and the particular proton jump path within a given zeolite. Proton tunneling effects appear to be negligible above room temperature. The calculated reaction barriers vary between 52 and 106 kJ/mol. While in all three zeolites both low and high barriers exist, the special structural features of the zeolite frameworks allow the prediction that the proton mobility is generally lower in chabazite and faujasite than in ZSM-5, in agreement with experimental data. Three structure factors determine the height of the barriers: (i) stabilization of the proton in the transition structure by interactions with neighboring oxygen atoms. (ii) local framework flexibility, which allows for narrowing of the O-Al-O angle without too much energy penalty, and (iii) overall flexibility of the zeolite lattice. The first two factors explain that proton jumps occurring between oxygen atoms in six-membered aluminosilicate rings have the lowest barriers. Jumps between oxygen atoms in four-membered rings and oxygen atoms in open zeolite channels or cavities have high barriers. The larger overall flexibility of the ZSM-5 lattice makes barriers for jumps occurring within a ring of a given size in ZSM-5 generally lower than in chabazite and faujasite.