Working memory (WM) consists of short-term storage and executive components. We studied cortical oscillatory correlates of these two components in a large sample of 156 participants to assess separately the contribution of them to individual differences in WM. The participants were presented with WM tasks of above-average complexity. Some of the tasks required only storage in WM, others required storage and mental manipulations. Our data indicate a close relationship between frontal midline theta, central beta activity and the executive components of WM. The oscillatory counterparts of the executive components were associated with individual differences in verbal WM performance. In contrast, alpha activity was not related to the individual differences. The results demonstrate that executive components of WM, rather than short-term storage capacity, play the decisive role in individual WM capacity limits.