We have used one and two dimensional exchange 1H NMR spectroscopy to characterize the dynamics of the binding of a homodimeric thiazole orange dye, 1,1'-(4,4,8,8-tetramethyl-4,8-diaza-undecamethylene)-bis- 4-(3-methyl-2,3-dihydro-(benzo-1,3-thiazole)-2-methylidene)-quinol inium tetraiodide (TOTO), to double stranded DNA (dsDNA). The double stranded oligonucleotides used were d-(CGCTAGCG)2 (1) and d(CGCTAGCTAGCG)2 (2). TOTO binds preferentially to the (5'-CTAG-3')2 sites and forms mixtures of 1:1 and 1:2 dsDNA-TOTO complexes with 2 in ratios dependent on the relative amount of TOTO and the oligonucleotide in the sample. The dynamic exchange between preferential binding sites in the case of a 2:1 1-TOTO mixture is an intermolecular exchange process between two binding sites on different oligonucleotides. In the case of the 1:1 2-TOTO complex an intramolecular exchange process occur between two different binding sites on the same strand. Both processes were studied. The results demonstrate the ability of TOTO to migrate along a dsDNA strand in an intramolecular exchange process. The migration process ("creeping") along the DNA strand is 6 times faster than the rate of intermolecular exchange between sites in two different oligonucleotides.