It has been shown, theoretically and experimentally, that a hole or an excess electron on a DNA molecule in solution forms a delocalized wave function, a polaron. For an all-adenine (A) sequence or a mixed sequence of guanines (G's) and A's, calculations taking into account the polarization of the solution give the wave function spread over approximately four bases, which appears to be in agreement with experiment. The polaron may move by hopping or by drift. Drift can take place in a region with all the same bases, for example, A's, by the polaron dropping an A on the trailing edge and picking up an A on the leading edge. For drift that is not too rapid, the necessity of the polarization changing as the polaron moves exerts a drag on the polaron. We calculate the drag by using a model introduced earlier to describe the polaron. We find the drag to be proportional to the velocity of the polaron and to the orientational relaxation time of the water molecules. The drag is also a function of the Coulomb interactions of the fractional charges on the bases constituting the polaron, as modified by the polarization charge induced in the solution. The diffusion rate and mobility for all A polarons, calculated taking into account the drag, are 8 x 10(-5) cm(2)/s and 3 x 10(-3) cm(2)/(Vs), respectively. We believe that in the experimental studies that have been carried out on hole propagation in a series of A's it was drift being observed rather than the hopping of a localized hole between adjacent A's, as was assumed to be the case.