We analyzed test-retest reliability of Absolute (AP) and Relative Power (RP) during rest and during two cognitive tasks: one verbal, the search for a synonym, and the other consisting of mental arithmetic calculations. Under all conditions during the experiment the subjects had their eyes open. The experiment was performed twice, with a month's interval between each trial. Monopolar recordings were obtained in F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6 and Cz vs A1A2. Differences between sessions were observed mainly during rest with eyes open in the lapha band, with higher AP during the first session. During rest it is extremely difficult to control for the state of vigilance, anxiety and thinking. However, during cognitive tasks a more rigid control of the state of vigilance and thinking is obtained. Therefore, AP and RP are very reliable parameters for analyzing EEG during mental tasks. Comparisons between conditions were also made. The only significant differences observed were in delta AP in the second session, with more power during the cognitive tasks in C3 and O2. MANOVAs using the values of AP in the four bands showed significant differences between conditions in C3, C4, P3, O2 and T4. Several factors that may be involved in the origin of delta activity, including eye movements, slow potential shifts and the inhibition of cholinergic projections to the cortex, are discussed.