INCE a formal characterization of the nature of inversions has not been made to date, this paper will hypothesize mathematical models for the occurrence of inversions of various lengths, obtain the associated probability distributions of lengths and midpoints of chromosomal inversions, and compare the hypothesized models with two sets of data. A study of the departures from hypothesized models should throw light on the mechanisms of the origin of inversions with respect to their distribution along the chromosome.