Background: Both transactional and common etiological models have been proposed as explanations of why externalizing behavior problems (EBP) and internalizing behavior problems (IBP) co-occur in children. Yet little research has empirically evaluated these competing theoretical explanations. We examined whether EBP and IBP are transactionally related at the within-child level while also identifying antecedents commonly associated with between-child differences in underlying stability of both EBP and IBP across elementary school. Methods: We analyzed a nationally representative and longitudinal sample of US schoolchildren (N = 7,326; 51% male) using random-intercept cross-lagged panel modeling (RI-CLPM). We used teacher ratings of EBP and IBP as annually assessed from the spring of kindergarten (M[subscript age] = 6.12 years) through the spring of 5th grade (M[subscript age] = 11.09 years). Early childhood antecedents included child internal (i.e. inhibitory control, cognitive flexibility, working memory, and language/literacy) and external factors (i.e. parental warmth, harsh parenting, parenting stress, and maternal depressive symptoms). Results: We found little evidence for within-child, transactional relations between EBP and IBP. Both types of behavior problems instead were substantially associated at the between-child level. Inhibitory control was the strongest common antecedent that explained this longitudinal overlap. Cognitive flexibility, working memory, language/literacy skills, and maternal depression contributed specifically to the stability of IBP. Measures of parenting were specific to the stability of EBP. Conclusions: Common etiological factors rather than transactional relations better explain the co-occurrence of EBP and IBP during elementary school. Inhibitory control is a promising target of early intervention efforts for schoolchildren at risk of displaying both EBP and IBP. [This is the online first version of an article published in "Journal of Child Psychology and Psychiatry."]