The paper examines the dynamical behavior of a radical cation (G+*) generated in a double stranded DNA for different oligonucleotide sequences. The resonance hole tunneling through an oligonucleotide sequence is studied by the method of numerical integration of self-consistent quantum-mechanical equations. The hole motion is considered quantum mechanically and nucleotide base oscillations are treated classically. The results obtained demonstrate a strong dependence of charge transfer on the type of nucleotide sequence. The rates of the hole transfer are calculated for different nucleotide sequences and compared with experimental data on the transfer from (G+*) to a GGG unit.