This article deals with the application of methods from the theory of nonlinear dynamical systems to EEG signals. Theoretical background, mathematical concepts and algorithms for the calculation of "non-linear parameters" are reviewed and influences of the structure of reconstructed data sets on the calculations are pointed out. We present results for the estimation of the correlation dimension D2 and the principal Lyapunov-exponent lambda 1 for sleep EEG data respectively from 10 and 15 healthy subjects corresponding to different sleep stages. Essentially, we found a statistically significant decrease of both D2 and lambda 1 as sleep moves towards slow wave stages. The values for REM sleep lie between the values of stage I and II. Moreover, for one subject as an example we present calculations of the principal Lyapunov-exponent lambda 1 and the sum of the two largest Lyapunov-exponents lambda 1 + lambda 2 for EEG segments following subsequently during the night. Finally, we compare our results with investigations of other groups and discuss difficulties and opportunities of the nonlinear approach to human EEG signals.