Cytological analysis of the thelytokous soft-scale insects Coccus hesperidum L. (2n=14) and Saissetia coffeae (Walker) (2n=16) revealed that while in both “species” the chromosomes did not pair during prophase I, meiosis consisted of two divisions, the chromosome number was reduced, and diploidy was restored by the fusion of the female pronucleus with the polar nucleus II. The difficulty of trying to classify this type of thelytoky as either automictic or apomictic led to the proposal that a new criterion and new terms be used to classify thelytoky (and parthenogenesis). The new criterion is whether the number of chromosome elements present in the first (or only) metaphase of oogenesis is the same as that present in the oogonia (gonoid thelytoky) or different from it (agonoid thelytoky). The new criterion is superior to the existing criteria because it is unambiguous, and because it groups together forms with a similar tendency towards heterozygosity (or homozygosity). The possible evolution of the forms analyzed as well as the two other thelytokous forms of each “species” described by Thomsen (1927) are discussed. Another soft-scale insect, Physokermes hemicryphus Dalam, consisted of a diploid (2n=18) and a triploid (3n=27) form, in both of which the chromosomes also did not pair. Each of the three “species” contained a strain in which only a single nucleolus was present per cell. In C. hesperidum some strains with two nucleoli differed in the size of the nucleoli.