We present transfer rates for the concerted hydrogen exchange in cyclic water clusters (H2O)(n) (n=3,4) based on ab initio hypersurfaces. The studied hydrogen exchange involves bond breaking and forming and is in contrast to flipping motions of "free" hydrogen atoms in a "chemical" reaction. The rates are calculated for gas-phase systems using canonical, variational transition state theory. Multidimensional tunneling corrections are included assuming both a small and a large reaction path curvature. Hybrid density functional theory [B3LYP/6-31+G(d)] was used to evaluate the potential energy hypersurface with interpolated corrections of second order perturbation theory [MP2/6-311+ +G(3pd,3df)] at the three stationary points for both systems. Large curvature tunneling corrections are included in dual-level direct ab initio dynamics for the cyclic tri- and tetramer of water. The ridge of the reaction swath serves as an estimate for the tunneling probability of various straight-line corner cutting paths. Our results suggest that the investigated species interconvert on a time scale of seconds. The ground-state tunneling splitting is proportional to the square root of the transition probability at the energy of the minima, which is available from the calculation of tunneling corrections. The associated tunneling splittings are estimated to be between 10(-4) and 10(-5) cm(-1), which is close to the experimental resolution limit.