Relatively little is known about episodic memory (EM: memory for personally-experienced events) and prospective memory (PM: memory for intended actions) in children born very preterm (VP) or with very low birth weight (VLBW). This study evaluates EM and PM in mainstream-schooled 7- to 9-year-olds born VP (≤ 32 weeks) and/or VLBW (< 1500 g) and matches full-term children for comparison (n = 35 and n = 37, respectively). Additionally, participants were assessed for verbal and non-verbal ability, executive function (EF), and theory of mind (ToM). The results show that the VP/VLBW children were outperformed by the full-term children on the memory tests overall, with a significant univariate group difference in PM. Moreover, within the VP/VLBW group, the measures of PM, verbal ability and working memory all displayed reliable negative correlations with severity of neonatal illness. PM was found to be independent of EM and cognitive functioning, suggesting that this form of memory might constitute a domain of specific vulnerability for VP/VLBW children.