We examined parent and child moderators of outcome, program engagement effects, and predictors of engagement in the Incredible Years Parent Training Program. Head Start classrooms (N = 882 children) were randomly assigned to an intervention condition (that received the Incredible Years program) or to a control condition (that received usual Head Start services). Structural equation modeling (SEM) was used to model the effects of the training program on child outcomes. The analyses showed differential program effects depending on children's initial levels of conduct problems and mothers' initial levels of critical parenting. Children with high baseline levels of conduct problems and children of mothers with high initial levels of critical parenting benefited most from the program. Changes in children's conduct problems were also related to maternal engagement in the program and to intervention mothers' success at reducing their critical parenting.