The problems of the classification and evolution of the rodents continue to provide a basis for disagreement among students of the group. This is because of the considerable number of forms involved, and because of the unquestioned parallelism which has occurred in the evolution of members of the order. Even those authors who question parallelism in other structures admit that it occurs in the tooth patterns, and the present author believes it has been characteristic of all aspects of rodent morphology. There are many current problems which will be elucidated as more work is done, both on fossil and on Recent rodents. Until a great deal more of such work is carried out, the classification of the order cannot be anything but tentative. Nevertheless, such tentative classifications serve a value as showing areas where further investigations are needed, and in stimulating discussion, and the present paper is presented with this in mind. For many years, most workers grouped the rodents inlto the three Brandtian suborders -Sciuromorpha, Myomorpha and Hystricomorpha (cf. Simpson, 1945) or some variant thereof (Tullberg, 1899). In the past few years, however, almost everyone working primarily with rodent taxonomy has expressed his firm conviction that these three suborders are not valid phyletic entities (see, for example, Lavocat, 1951, 1955, 1956; Schaub, 1953, a and b; Viret, 1955; and Wood, 1954, 1955). But almost everyone who has approached this question has come up with