We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic and nonlinear deterministic methods. We propose, in a first step to segment the EEG time series into piecewise quasi-stationary epochs by means of nonparametric change point analysis. Subsequently, nonlinear measures can be estimated with higher confidence for the segmented epochs fullfilling the stationarity condition.