In this work the mechanism of migration of positive charges through donor-DNA-acceptor systems is studied using a quantum mechanical model based on the tight-binding approximation. For DNA bridges containing only adenine-thymine (AT) base pairs the difference in ionization potential between the donor moiety and the AT base pairs (i.e., the injection barrier) is shown to determine the mechanism by which the charge migrates from the donor to the acceptor. For an injection barrier of 0.55 eV, corresponding to a guanine radical cation as the hole-donor, a beta -value of 0.85 Angstrom (-1) is found. This agrees reasonably with the value of beta = 0.7 Angstrom (-1) deduced from experimental studies on these sequences. For this injection barrier (0.55 eV) the charge density on the AT bridge was found to be very small, which is characteristic for charge transfer by single-step tunneling. For lower injection barriers the charge density on the AT bridge becomes substantial and the charge moves through the bridge according to a bandlike mechanism. The actual DNA base pair sequence is shown to have a large effect on the charge transport mechanism. For a series of DNA bridges with an increasing number of guanine-cytosine (GC) base pairs, mutually separated by 2 AT base pairs a weak distance dependence is found in agreement with experimental data for these sequences. It is shown that the charge migration mechanism is effectively hopping between GC base pairs.