A neural network based technique is presented, which is able to successfully extract polynomial classification rules from labeled electroencephalogram (EEG) signals. To represent the classification rules in an analytical form, we use the polynomial neural networks trained by a modified Group Method of Data Handling (GMDH). The classification rules were extracted from clinical EEG data that were recorded from an Alzheimer patient and the sudden death risk patients. The third data is EEG recordings that include the normal and artifact segments. These EEG data were visually identified by medical experts. The extracted polynomial rules verified on the testing EEG data allow to correctly classify 72% of the risk group patients and 96.5% of the segments. These rules performs slightly better than standard feedforward neural networks.