  We study the high-energy behavior of the scattering amplitudes in quantum
electrodynamics beyond the leading order of the small electron mass expansion
in the leading logarithmic approximation. In contrast to the Sudakov
logarithms, the mass-suppressed double-logarithmic radiative corrections are
induced by a soft electron pair exchange and result in enhancement of the
power-suppressed contribution. Possible applications of our result to the
analysis of the high-energy processes in quantum chromodynamics is also
discussed.
