Kuhn's model of the structure of scientific revolutions, Popper's hypothetic-deductive model of science, and Lakatos's methodology of competing research programs are applied to a historical episode in biology. Each of these three models offers a different explanatory system for the development, neglect, and eventual acceptance of Mendel's paradigm of inheritance. The authors conclude that both rational and nonrational criteria play an important role during times of crisis in science, when different research programs compete for acceptance. It is suggested that Kuhn's model, emphasizing the nonrational basis of science, and Popper's model, emphasizing the rational basis of science, can be used fruitfully in high school science courses.