Decades of research have established that "online" cognitive processes, which operate during conscious encoding and retrieval of information, contribute substantially to individual differences in memory. Furthermore, it is widely accepted that "offline" processes during sleep also contribute to memory performance. However, the question of whether individual differences in these two types of processes are related to one another remains unanswered. We investigated whether working memory capacity (WMC), a factor believed to contribute substantially to individual differences in online processing, was related to sleep-dependent declarative memory consolidation. Consistent with previous studies, memory for word pairs reliably improved after a period of sleep, whereas performance did not improve after an equal interval of wakefulness. More important, there was a significant, positive correlation between WMC and increase in memory performance after sleep but not after a period of wakefulness. The correlation between WMC and performance during initial test was not significant, suggesting that the relationship is specific to change in memory due to sleep. This suggests a fundamental underlying ability that may distinguish individuals with high memory capacity. (Contains 3 figures and 1 table.)