Neurophysiological measurements obtained from e.g. EEG or fMRI are inherently non-stationary because the properties of the underlying brain processes vary over time. For example, in Brain-Computer-Interfacing (BCI), deteriorating performance (bitrate) is a common phenomenon since the parameters determined during the calibration phase can be suboptimal under the application regime, where the brain state is different, e.g. due to increased tiredness or changes in the experimental paradigm. We show that Stationary Subspace Analysis (SSA), a time series analysis method, can be used to identify the underlying stationary and non-stationary brain sources from high-dimensional EEG measurements. Restricting the BCI to the stationary sources found by SSA can significantly increase the performance. Moreover, SSA yields topographic maps corresponding to stationary- and non-stationary brain sources which reveal their spatial characteristics.