In this chapter we describe new neural-network techniques developed for visual mining clinical electroencephalograms (EEGs), the weak electrical potentials invoked by brain activity. These techniques exploit fruitful ideas of Group Method of Data Handling (GMDH). Section 2 briefly describes the standard neural-network techniques which are able to learn well-suited classification modes from data presented by relevant features. Section 3 introduces an evolving cascade neural network technique which adds new input nodes as well as new neurons to the network while the training error decreases. This algorithm is applied to recognize artifacts in the clinical EEGs. Section 4 presents the GMDH-type polynomial networks learnt from data. We applied this technique to distinguish the EEGs recorded from an Alzheimer and a healthy patient as well as recognize EEG artifacts. Section 5 describes the new neural-network technique developed to induce multi-class concepts from data. We used this technique for inducing a 16-class concept from the large-scale clinical EEG data. Finally we discuss perspectives of applying the neural-network techniques to clinical EEGs.