The three-body interaction energy in the (H2O)(2)H-2 cluster is evaluated using the supermolecular Moller-Plesset perturbation theory and analyzed in terms of the perturbation theory of intermolecular forces. Four main configurations are investigated in which the H-2 molecule is attached to either the O or H atoms of the water dimer. In these structures nonadditivity originates mainly from the induction effect. The exchange and dispersion nonadditivities are of secondary importance. The overall three-body effect can be reasonably well reproduced at the uncorrelated level. The water...water hydrogen bond is reinforced when its proton donor moiety acts as the hydrogen bond acceptor with respect to the H-2 molecule and when the acceptor moiety acts as a hydrogen bond donor. On the other hand, the water water hydrogen bond is weakened when the donor water molecule behaves as a double donor or the acceptor water as a double acceptor.