We have studied the effect of fluctuating structural distortions on the efficiency of hole migration in some DNA double strands. Standard molecular dynamics (MD) simulations of DNA embedded in water have been performed over a time intervals of 40 ps. The MD study was followed by quantum chemical calculations of time-dependent electronic coupling between all the pairs of adjacent bases and by the subsequent evaluation of the fluctuating, effective electronic coupling between donor and acceptor (H-DA) guanine bases. A convenient parametrization of the coupling in terms of the overlap between the localized wave functions was found by a large number of ab initio calculations. The MD results show that HDA undergoes large fluctuations and that its quadratic average is 1 order of magnitude larger than its mean value. Furthermore, the MD analysis shows that the base-pair couplings are due predominantly to the transverse motions of the DNA strands, while longitudinal motions are surprisingly ineffective.