This article extends the work of Kellam, Ling, Merisca, Brown and Ialongo (1998) by applying a mathematical model of competition between children to peer contagion in the aggressive behaviors of elementary school students. Nonlinearity in the relationship between group aggression and individual aggression at 2-year follow-up is present. Consistent with the findings of Kellam et al. (1998), hierarchical linear modeling indicates that the relationship is statistically significant for those students whose initial parental ratings of aggressive behavior were above the sample median. In the context of competition between students, the behavior of initially aggressive students may be negatively reinforced. Lowering aggression in the school environment may therefore be the most effective way to lower the level of these students' aggressive behavior.