This study examined the relation of information processing in 7-month-old preterms (<1750 g at birth) and full-terms to Bayley Mental Development Indexes (MDIs) at 2 and 3 years. The infant measures were drawn from four cognitive domains: attention, speed, memory, and representational competence. Structural equation modeling showed that these measures of infant information processing mediated the effects of prematurity, and that there was a cascade of effects, with infant processing speed influencing memory and representational competence, which in turn influenced later MDI. This study shows that infant information processing mediates the effect of prematurity on later cognition, and delineates pathways whereby infant abilities relate to one another and to later outcome.