Many recent studies based on the surrogate data method failed to identify significant non-linearity in the EEG. In this study we examine whether the use of a different embedding method (spatial instead of time delay), and calculation of Kolmogorov entropy (K2) and the largest Lyapunov exponent (L1) in addition to the correlation dimension (D2), can distinguish the EEG form linearly filtered noise. We have calculated D2, L1 and K2 of original EEG epochs and surrogate (phase randomized) data in 9 control subjects, 9 demented patients and 13 Parkinson patients. The correlation dimension D2 and the largest Lyapunov exponent L1 could distinguish between the EEG tracings and the surrogate data. Demented patients had significantly lower D2 and L1 compared to controls. L1 was higher in Parkinson patients than in demented patients. Contrary to other studies that have used the Theiler surrogate data method, we find evidence for non-linearity in normal and abnormal EEG during the awake/eyes closed state. Apparently it is the spatial structure in the EEG that exhibits much of the non-linear structure. Furthermore, non-linear EEG measures show more or less specific patterns of dysfunction in dementia and Parkinson's disease.