Multichannel EEG as sequence of momentary brain field maps constitutes a trajectory through K-dimensional state space (K = number of channels); the complexity of this trajectory is assessed by the nonlinear measure of global correlation dimension (Global Dimensional Complexity, GDC) with the number of electrodes as embedding dimension. We analyzed eyes-closed EEG of three age-matched subject groups: mild Alzheimer's disease (AD; n = 21), mild cognitive impairment (29) and subjective memory complaint (29). Kruskal-Wallis statistics showed an overall effect between groups. AD patients differed significantly (GDC = 4.56) from mild cognitive impairments (GDC = 4.98) and from subjective memory complaints (GDC = 4.93). GDC also had significant positive correlations with mental condition and performance (MMSE and WAIS-R scores). Thus, the dynamics of brain state development over time in mild AD differs from that in mild cognitive impairment and in subjective memory complaint cases.