During study trials of a recognition memory task, alpha (∼10 Hz) oscillations decrease, and concurrently, theta (4-8 Hz) oscillations increase when later memory is successful versus unsuccessful (subsequent memory effect). Likewise, at test, reduced alpha and increased theta activity are associated with successful memory (retrieval success effect). Here we take an individual-differences approach to test three hypotheses about theta and alpha oscillations in verbal, old/new recognition, measuring the difference in oscillations between hit trials and miss trials. First, we test the hypothesis that theta and alpha oscillations have a moderately mutually exclusive relationship; but no support for this hypothesis was found. Second, we test the hypothesis that theta oscillations explain not only memory effects within participants, but also individual differences. Supporting this prediction, durations of theta (but not alpha) oscillations at study and at test correlated significantly with d' across participants. Third, we test the hypothesis that theta and alpha oscillations reflect familiarity and recollection processes by comparing oscillation measures to ERPs that are implicated in familiarity and recollection. The alpha-oscillation effects correlated with some ERP measures, but inversely, suggesting that the actions of alpha oscillations on memory processes are distinct from the roles of familiarity- and recollection-linked ERP signals. The theta-oscillation measures, despite differentiating hits from misses, did not correlate with any ERP measure; thus, theta oscillations may reflect elaborative processes not tapped by recollection-related ERPs. Our findings are consistent with alpha oscillations reflecting visual inattention, which can modulate memory, and with theta oscillations supporting recognition memory in ways that complement the most commonly studied ERPs.