Current theories of intellectual development claim that such development proceeds through invariant sequences of increasingly more adequate cognitive structures. According to the two dominant theories on changes in intellectual functioning during adulthood, intellectual development is essentially accomplished by adolescence, although sharpening and application of these abilities and skills continues in new content areas. The longitudinal approach required for such research, however, suffers from a number of unique methodological difficulties. For instance, the longitudinal approach tends to confuse individual change with historical change and is particularly prone to sampling bias. An examination of longitudinal studies dealing with sequences of intellectual development during the college years reveals a number of methods that life-span developmental theorists have developed to deal with the methodological difficulties of age-change research. Included among these are the cross-sectional sequence, the time-lag sequential, and the longtudinal-sequential methods. Another approach, the Reflective Judgment (RJ) Model presents seven stages of intellectual development that reflect different assumptions about knowledge and reality that underlie different ways in which beliefs are justified. Three studies that follow this model support the claim that the RJ level increases with education and that intellectual development in the college years follows a predicted sequence. (MN)