During recent years, methods from nonlinear dynamics were introduced into the analysis of EEG signals. Although from a theoretical point of view nonlinear measures quantify properties being independent from conventional spectral measures, it is a crucial question whether in practice nonlinear EEG measures yield additional information, which is not redundant to the information gained by spectral analysis. Therefore, we compared the ability of several spectral and nonlinear measures to discriminate different sleep stages. We evaluated spectral measures (relative delta power, spectral edge, spectral entropy and first spectral moment), and nonlinear measures (correlation dimension D2, largest Lyapunov exponent LI, and approximated Kolmogorof entropy K2), and additionally the stochastic time domain based measure entropy of amplitudes. For 12 healthy subjects these measures were calculated from sleep EEG segments of 2:44 min duration, each segment unambiguously corresponding to one of the sleep stages I, II, SWS and REM. Results were statistically evaluated by multivariate and univariate analyses of variance and by discriminant analyses. Generally, nonlinear measures (D2 and L1) performed better in discriminating sleep stages I and II, whereas spectral measures showed advantages in discriminating stage II and SWS. Combinations of spectral and nonlinear measures yielded a better overall discrimination of sleep stages than spectral measures alone. The best overall discrimination was reached even without inclusion of any of the spectral measures. It can be concluded that nonlinear measures yield additional information, which improves the ability to discriminate sleep stages and which may in general improve the ability to distinguish different psychophysiological states. This confirms the importance and practical reliability of the application of nonlinear methods to EEG analysis.