The topological state of genomic DNA is of importance for its replication, recombination and transcription. The wrapping of the DNA around nucleosomes is associated with sequence periodicities (Trifonov and Sussman, Proc. Natl. Acad. Sci. USA, 77, pp. 3816-20). Recently, also the negative supercoiling of eubacterial DNA was related to 11 base pair (bp) periodicity (Herzel et al. Physica A, 249, pp. 449-59). Archaeal plasmids and a virus-like particle from Sulfolobus are positively supercoiled, but the superhelical conformation of archaeal genomic DNA is still uncertain. The problem of superhelicity can now be addressed via a comparative statistical analysis of the available complete genomes. For this purpose one has to look for periodicities which are in phase with the helical repeat of 10-11 bp. Similar periodicities are induced, however, by the amphipatic character of alpha-helices of encoded proteins (Zhurkin, Nucl. Acids Res., 9, pp. 1963-71). We show that these protein-induced periodicities are extended over a few periods only. The periods of additional long-ranging oscillations deviate significantly from the value for free DNA. A period of 11 bp in Eubacteria reflects negative supercoiling, whereas the significantly different period of thermophilic Archaea close to 10 bp suggests positive supercoiling of archaeal genomes.