Simple repetitive DNA sequences are a widespread and abundant feature of genomic DNA. The following several features characterize such sequences: (1) they typically consist of a variety of repeated motifs of 1-10 bases--but may include much larger repeats as well; (2) larger repeat units often include shorter ones within them; (3) long polypyrimidine and poly-CA tracts are often found; and (4) tandem arrangements of closely related motifs are often found. We propose that slipped-strand mispairing events, in concert with unequal crossing-over, can readily account for all of these features. The frequent occurrence of long tandem repeats of particular motifs (polypyrimidine and poly-CA tracts) appears to result from nonrandom patterns of nucleotide substitution. We argue that the intrahelical process of slipped-strand mispairing is much more likely to be the major factor in the initial expansion of short repeated motifs and that, after initial expansion, simple tandem repeats may be predisposed to further expansion by unequal crossing-over or other interhelical events because of their propensity to mispair. Evidence is presented that single-base repeats (the shortest possible motifs) are represented by longer runs in mammalian introns than would be expected on a random basis, supporting the idea that SSM may be a ubiquitous force in the evolution of the eukaryotic genome. Simple repetitive sequences may therefore represent a natural ground state of DNA unselected for coding functions.