Wrangham (1980) hypothesized that knowledge of the nature of intergroup encounters is crucial to understanding primate social relationships and social organization. I studied a single social group of wild white-faced capuchins over a period of 26 months and observed 44 encounters between social groups during 3703 hr of observation. All intergroup encounters consisted of predominantly hostile social interactions. However, nonaggressive interactions between males of different social groups occurred in a few cases. Adult males were the sole participants in 39 encounters and the primary participants in all 44 encounters. The alpha male was the most frequent participant. High-ranking females participated aggressively in five encounters, and low-ranking females never participated. There was no stable intergroup dominance hierarchy. I hypothesize that the need for male-male cooperation in intergroup aggression is an important factor influencing the quality of intragroup male-male relationships. Behavior during intergroup encounters is consistent with the idea that intergroup behavior is related to male reproductive strategies, but inconsistent with the idea that intergroup aggression is related to female defense of resources. The possibility that males are “hired guns” (Wrangham, 1980) cannot be ruled out.