The purpose of study was to investigate the longitudinal relations among maternal supportiveness, child task-approach behavior, and cognitive development for children with developmental risks. The participants (N = 400) in this study were a subset of the National Early Head Start Research and Evaluation Project. The current study used structural equation modeling analyses including growth-curve models.;Findings are that maternal supportiveness was moderately stable from the time the children were 14 to 36 months of age, but stability of child task-approach behavior was weak between 14 and 24 months of age. Child task-approach behavior became stronger as children grew older. Earlier maternal supportiveness influenced later child task-approach behavior, but earlier child task-approach behavior did not influence later maternal supportiveness. Child task-approach behavior across time influenced the initial level of child cognition and the rate of cognitive development from 14 to 36 months of child age. Earlier maternal supportiveness influenced the initial level of child cognition, and later maternal supportiveness influenced the rate of cognitive development. Maternal education and age were positively related to maternal supportiveness. The initial level of child cognition and earlier child task approach behavior were related negatively to the rate of cognitive development.;This study provides evidence that mothers' supportive interactions are important in children's cognitive development, as well as their task-approach behaviors, and children's task approach behaviors influence their rate of cognitive development. These findings support providing intervention services for low-income mothers, especially those who are young or less well educated in order to enhance their interactions with their children. Also, this study supports the potential utility of improved capabilities for the early diagnosis of developmental delays and more sensitive eligibility criteria for early intervention services.