Simultaneous recording of electroencephalogram/functional magnetic resonance images (EEG/fMRI) was applied to identify blood oxygenation level-dependent (BOLD) changes associated with spontaneous variations of the alpha rhythm, which is considered the hallmark of the brain resting state. The analysis was focused on inter-subject variability associated with the resting state. Data from 7 normal subjects are presented. Confirming earlier findings, three subjects showed a negative correlation between the BOLD signal and the average power time series within the alpha band (8--12 Hz) in extensive areas of the occipital, parietal and frontal lobes. In small thalamic areas, the BOLD signal was positively correlated with the alpha power. For subjects 3 and 4, who displayed two different states during the data acquisition time, it was shown that the corresponding correlation patterns were different, thus demonstrating the state dependency of the results. In subject 5, the changes in BOLD were observed mainly in the frontal and temporal lobes. Subject 6 only showed positive correlations, thus contradicting the negative BOLD alpha power cortical correlations that were found in most subjects. Results suggest that the resting state varies over subjects and, sometimes, even within one subject. As the resting state plays an important role in many fMRI experiments, the inter-subject variability of this state should be addressed when comparing fMRI results from different subjects.