Inverted repeat sequences, capable of forming stable intra-chain foldback duplexes, are shown using electron microscopy to be located in over 90% of fragments of nuclear DNA from Physarum polycephalum. A statistical treatment of the data indicates that, on average, foldback sequence foci are spaced every 7,000 nucleotides and that they are distributed uniformly amongst the DNA chains. The majority of inverted repeat sequences give rise to the simple types of foldback structure observed in DNA from other eukaryotic species, but a significant proportion of the DNA fragments also contain novel foldback structures with a more complex appearance, referred to as 'bubbled' hairpins. The latter structures appear to be formed by the annealing of several distinct segments of homologous inverted repeat sequence, each separated by interspersed non-foldback sequences of variable sizes up to 15,000 nucleotides in length. The size, both of the foldback duplexes and of the intervening single-chain segments of DNA, are not random. Instead, they appear to form a regular, arithmetic series of lengths. These observations suggest that the different segments of Physarum DNA from which foldback structures are derived contain nucleotide sequences that share a highly ordered and unform pattern of structural organisation. These regular units of organisation in Physarum DNA in some cases extend over distances up to 50,000 nucleotides in length.