The interspersed periodic arrangement of repetitive and unique sequences in eukaryotic DNAs is proposed as the underlying molecular basis for higher-order DNA coiling in chromatin and mitotic chromosomes. It is assumed that (i) two types of interspersed repetitive sequences are distributed strictly periodically throughout the genome, splitting the single copy DNA into short and long periods respectively in such a pattern that each long period is composed of a definite number of short periods and repeats, (ii) the short and long periods make the turn lengths of the solenoid and supersolenoid structures respectively determining their diameters; (iii) specific proteins interact with each type of repeats making cross ties between nearby repeats of each class helping to form, constrain, and stabilize the solenoid and the supersolenoid structures: (iv) the long period may be equated with the basic chromomere unit. The model predicts: (i) splitting of contiguous genes by inserted repetitive sequences; and (ii) two types of genomes differing in the hierarchy of DNA coiling.