Abstract: Excessive alcohol use and binge drinking among college students are health risk behaviors of significant concern. Two important correlates of this behavior, alcohol use attitudes and peer pressure, are often examined within the context of the model offered by the Theory of Reasoned Action. While this model has yielded valuable insights, an intriguing new line of research emerging from the field of nonlinear dynamics is offering to extend our understanding of this behavior. Preliminary findings in the literature suggest that cusp catastrophe modeling may provide a more sophisticated method for understanding students' substance use behavior by accounting for relatively simple but important nonlinear relationships between substance use, attitudes, and peer pressure. This study therefore examined whether a cusp catastrophe model (CCM) would more effectively explain patterns of alcohol use among college students than either a simple linear statistical model or a linear interaction model. This study used archival data collected on 1,197 undergraduates who completed the Core Alcohol and Drug Survey. The effectiveness of the nonlinear model was determined by contrasting it with the findings from two linear statistical models. Separate series of analyses were performed for each of the three dependent variables examined in this study—binge drinking, frequency of alcohol use, and quantity of alcohol use. A major finding of this dissertation was the success of the CCM in capturing the nonlinear dynamics that influenced the binge drinking and other alcohol use behavior of the college undergraduates. Analyses revealed that for both males and females the CCM was better able to account for the relationship between attitudes, peer pressure, and frequency of binge drinking than the two linear models. The CCM also emerged as superior to the linear models in explaining quantity and frequency of alcohol use among college males. The findings of this study hold important implications both for understanding the complex behavioral effects of peer pressure on students' drinking behavior and for developing more effective interventions. The findings are also important in extending cusp catastrophe modeling of alcohol use to a college student population, thus adding to the emerging body of literature.