A theory is given of the process of chromosomal structural rearrangement following irradiation. The theory applies to nuclei in which the union of breakage ends is at random, and assumes that the number of breaks primarily produced is proportional to the dose. Formulae and tables are given enabling the proportion of nuclei undergoing eucentric and dyscentric types of rearrangement respectively to be calculated as a function of the dose, the cases of nuclei with 1, 2, 3, 4, 5, or many chromosome, arms in the set being separately considered. The five-arm calculation is compared with published experimental results of the irradiation of the spermatozoa ofDrosophila melanogaster.