We have shown that, for reasonable values of the parameters, stationary polarons, i.e., radical anions or cations extended over 5-7 base pairs, depending on base sequence, can exist in DNA. Here we report the results of an investigation of the drift motion of the polarons aimed at determining whether their formation can lead to rapid motion of charges introduced on DNA stacks. Starting from the same tight-binding Hamiltonian, we have used two different techniques for giving the polarons the kinetic energy required to make them move. We have applied these to the cases of DNA duplexes made up of (i) a single base pair repeated and (ii) a random sequence of base pairs, although we avoided sequences in which two guanines are next to each other. We find that the time required to deform the stack to produce a polaron after a hole or an extra electron is inserted into a DNA stack with uniformly spaced bases is similar to4 ps. For a DNA duplex made from the repetition of a single base pair, both theoretical techniques show that the polaron can move continuously, retaining its shape. Under a small electric field, 5 x 10(3) V/cm, the polaron moves slowly, covering a distance of 7 bases in similar to 140 ps. For DNA made up of random bases, the center of the polaron can hop on a picosecond time scale between guanines or between a guanine and an adenine, separated by up to a few bases. The possibility that polaron motion could account for the rapid hole transit found by some researchers is discussed.