A variety of studies have shown that EEG alpha activity in the upper frequency range is associated with different types of cognitive processes, memory performance, perceptual performance and intelligence, but in strikingly different ways. For semantic memory performance we have found that resting or reference power is positively associated with performance, whereas during actual processing of the task, small power--reflected by a large extent of event-related desynchronization (ERD)--is related to good performance. We also have shown that the induction of large alpha reference power by neurofeedback training or repetitive transcranial magnetic stimulation (rTMS) at individual alpha frequency mimicked exactly the situation which is typical for good memory performance under normal situations: increased alpha reference power is associated with large ERD and good performance. Recent studies have demonstrated that this relationship holds true only for memory and not perceptual tasks that require the identification of simple visual stimuli under difficult conditions. In contrast to good memory performance, good perceptual performance is related to small pre-stimulus alpha power and a small ERD. We interpret this finding in terms of cortical inhibition vs. activation preceding task performance by assuming that large rhythmic alpha activity reflects inhibition. We assume that small reference alpha enhances perceptual performance because the cortex is activated and prepared to process the stimulus, whereas memory performance is enhanced if the cortex is deactivated before a task is performed because in typical memory tasks selective processing can start only after the to-be-remembered item or cue is presented. We also suggest that conflicting results about alpha ERD and the neural efficiency hypothesis (which assumes that highly intelligent exhibit a small ERD) can also be interpreted in terms of inhibition. Only if an intelligence test actually requires the activation of (semantic) memory, a large (because task specific) ERD can be observed. If other processing systems are required, the semantic memory system may even become suppressed, which is reflected by alpha event-related synchronization (ERS) or at least a largely decreased ERD.