We study the high-energy small-angle Regge limit of the fermion-antifermion scattering in gauge theories and consider the part of the amplitude suppressed by a power of the scattering angle. For abelian gauge group all-order resummation of the doublelogarithmic radiative corrections to the leading power-suppressed term is performed. We find that when the logarithm of the scattering angle is comparable to the inverse gauge coupling constant the asymptotic double-logarithmic enhancement overcomes

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... the power suppression, a formally subleading term becomes dominant, and the small-angle expansion breaks down. In QCD we show that in the color-singlet channel for sufficiently small scattering angles the abelian power-suppressed contribution becomes comparable to the one of BFKL pomeron. Possible role of the subleading-power effects for the solution of the unitarity problem of perturbative Regge analysis in QED and QCD is discussed. An intriguing relation between the asymptotic behavior of the power-suppressed amplitudes in Regge and Sudakov limits is discovered.