The impedance spectra are measured for protonated and deuterated clathrates, HClO4.5.5H(2)O and DClO(4)5.5D(2)O, between 10 and 300 K. The conductance is investigated between 80 K and room temperature and the dielectric constant between 10 and 120 K. The data show deviation from the Arrhenius behavior of conductance in the low-temperature regime. A description of proton conductivity is developed on the basis of quantum theory of an elementary act of proton tunneling between donor-acceptor sites interacting with environmental fluctuations. Several models of the elementary act are considered. The mechanism, most consistent with the obtained data, incorporates-strong coupling of the proton with local vibrational modes of the closest environment and system diabatic transitions along these vibrational "coordinates"-fluctuations of the tunneling barrier for the proton. At low temperatures the motion along the vibrational coordinates is no longer purely classical and the slow mode tunneling takes place. The latter gives rise to a curvature in the Arrhenius plots apprehended as a decrease of the apparent activation energy at lower temperatures. The observed isotope effect is in line with the lower deuteron tunneling probability due to doubling the mass, though other parameters may also be affected by deuteration.