Using Hierarchical Linear Models (HLM) analysis, this study evaluated the effects of medical risk at birth and socioeconomic status (SES) on the rate of change in cognitive and social development over the first three years of life in premature children with low birth weight (LBW). Children with LBW (n = 79) with both high (HR) (n = 37) and low (LR) (n = 42) medical risk were compared to healthy full-term (FT) (n = 49) children. Children were assessed longitudinally at 6, 12, 24, and 36 months for cognitive development with the Bayley Scales of Infant Development and the McCarthy Scales for Children's Abilities, and for social initiative and responsiveness with observational measures. The HR LBW group had slower rates of increases in cognitive scores than did the LR LBW and FT groups and showed more deceleration in cognitive development by 36 months of age. Children with LBW, regardless of medical risk, had lower social initiating scores and slower rates of increase in initiating across the first 36 months than did FT children. As predicted, the groups did not show different rates of change for measures of social responsiveness. Higher SES was predictive of better cognitive and social development for all children. The difficulties encountered by children with LR and HR LBW in developing social initiating skills are discussed in relation to the link between learning to take initiative and early executive function skills.