The purpose of this study was the determination of the relationship between the dimensional complexity of the electroencephalogam (EEG) and the level of intelligence in humans. In two experiments 34 male subjects were divided into two groups, with high and low levels of intelligence (as measured by the intelligence quotient (IQ)). During a resting phase and various mental imagery conditions the EEG was recorded from several scalp sites. Nonlinear analysis, based on the theory of deterministic chaos, revealed that subjects with high IQs demonstrate higher dimensional complexity of the EEG attractors than subjects with low IQs only during resting conditions. During performance of the imagery tasks the less intelligent subjects increase the complexity of electrical brain dynamics such that IQ-dependency vanishes. The gross (mass) neuronal manifestation of general intelligence seems to depend on task conditions and may be related to the individual brain dynamics only when no specific task is present.