This paper introduces a neural network architecture for classifying feature vectors symbolizing portions (or segments) of an electroencephalogram (EEG) trace of a human subject. This classification task is the one that is typically required when developing a so-called brain-computer interface (BCI), which analyzes the EEG signals of a subject in order to "understand" the subject's thoughts. However, instead of merely saying which "category of thoughts" (i.e., which class) the respective input feature vector belongs to, the network described here estimates the probabilities of an EEG segment being associated with each individual class. The network, which is called PeGNC (for probability estimating guarded neural classifier), is tested with two kinds of experiments. In the first experiment, the alpha-rhythm associated with a human subject closing the eyes is detected online with the help of a frequency-based representation. Since the EEG signal is, in general, always a mixture of numerous action potentials generated simultaneously and it is, thus, very likely that mental activities result in overlapping classes, it is reasonable to believe that the PeGNC network--which does not select any one single class, but determines probability values for each mental category--is particularly suitable for this kind of EEG analysis. The second experiment deals with this issue on the basis of an offline analysis of simulated data.