Recent advances in the field of nonlinear dynamics have provided new conceptual models, as well as novel analytical techniques applicable to studies in alcohol research. One measurement technique, which has been developed in an attempt to characterize nonlinear systems in physics and biology, is the estimation of attractor dimension. This dimension may be seen as a measure of the information required to describe the current behavior of a system. We have applied these techniques to the analysis of EEG collected from 17 men with alcoholic fathers and 19 men with no alcoholic relatives. The men with alcoholic fathers were found to have a lower EEG attractor dimension than their matched controls. This suggests that the EEG of young men with alcoholic fathers may be "more organized" or "less complex" than men with no alcoholic relatives. Although more studies will be needed to explore this hypothesis, these studies suggest that further development of nonlinear approaches to the analysis of brain systems are likely to generate new clinical measures, as well as new ways of viewing brain electrical function and alcoholism.