A microscopic model for the description of the proton subsystem dynamics in
superionic crystals with hydrogen bonds is developed. Besides the inclusio
n of the proton-transport mechanism, the effect of the displacement of the
nearest oxygens during hydrogen-bond formation is taken into account. The l
atter effect is the cause of the strong proton-phonon coupling that leads t
o the polaronic effect. Using the occupation number formalism, the virtual
(in superionic phases) or ordered (in low-temperature phases) character of
the hydrogen-bonded system is taken into account on the basis of the proton
-ordering model. Protonic conductivity studies are carried out in the frame
work of the Kubo theory for the cases of superionic phases as well as low-t
emperature phases with different types of proton ordering (as an example th
e M3H(XO4)(2) class of crystals is considered). The temperature dependencie
s of the conductivity are analysed. The activation energies for the static
conductivity are determined; for this case the influence of the internal fi
eld which appears as a result of the proton ordering is investigated.