The proton conductivity in the hydrogen-bonded systems with strong correlations between protons is investigated theoretically in the context of the two-stage transport modeling approach. The distortions of the nearest ionic groups at the formation of the hydrogen bond are shown to be the reason for the strong proton-phonon coupling and polaronic effect. We evaluate as an example the conductivity for M3H(XO4)(2)-class of crystals with high proton mobility in (001) conducting planes. We analyze the temperature dependencies of the conductivity and its interbond and intrabond contributions in the vicinity of the transition from the disordered superionic to the ordered state. We investigate also the main peculiarities in the frequency dependencies of the conductivity appearing due to the proton interactions and compare our results with the previous conclusions obtained for the chains of noninteracting protons. (C) 2001 American Institute of Physics.