The dynamical model of tunneling interlevel transitions is extended to describe the kinetics of H-atom transfer in real reactions proceeding in the condensed phase. The reaction mechanism includes an explicit consideration of three modes; the high-frequency reactive motion of the H atom, the low-frequency intermolecular promotion mode, and an intramolecular mode which changes significantly during the reaction and is associated with the hybridization geometry changes of the reaction center. The rate constant expression is derived in terms of the standard technique of the theory of radiationless transitions. Its high- and moderate-temperature analysis reproduces the results obtained earlier in the framework of the Golden Rule approach. Peculiarities of the present theory are revealed beyond this temperature range. A remarkable low-temperature threshold effect causes steep temperature trends in the reaction rate which are likely to account for some recent kinetic experiments.