From the middle to the end of the 18th century, theses relating to fluxions occur on the Commencement broadsides of Harvard, Yale, and Rhode Island Colleges, as the probably do at other American colleges established by this time. These truths are sufficiently advanced in character to indicate that a real study of this subject was going on under the direction of a scholarly professor. In one case, Harvard, 1751, it is associated with the study of Newton's Principia. This beginning did not, perhaps, bear immediate fruit, for the first textbook prepared for use at Harvard contained no work on fluxions. Moreover, only one problem on fluxions is found before 1803 among the problems presented to the department of mathematics by the members of the junior and senior classes during the period 1782-1815, although the number increases thereafter. The notebook material of the period through the first quarter of the 19th century is limited to brief sections in several books and a single extended book. This complete treatment of the subject of fluxions has for its source Newton's own work rather than one of the several works o his imitators which appeared after his method became known. This study shows then the almost complete dominance of the great Newton himself in American schools as far as the subject of fluxions is concerned. By the end of the first quarter of the 19th century, the catalogue of at least one college, Yale, shows that fluxions had been accorded a place among electives for the student body.