A neurological disorder is one of the significant problems of the nervous system that affects the essential functions of the human brain and spinal cord. Monitoring brain activity through electroencephalography (EEG) has become an important tool in the diagnosis of brain disorders. The robust automatic classification of EEG signals is an important step towards detecting a brain disorder in its earlier stages before status deterioration. Motivated by the computation capabilities of natural evolution strategies (NES), this paper introduces an effective automatic classification approach denoted as natural evolution optimization-based deep learning (NEODL). The proposed classifier is an ingredient in a signal processing chain that comprises other state-of-the-art techniques in a consistent framework for the purpose of automatic EEG classification. The proposed framework consists of four steps. First, the L1-principal component analysis technique is used to enhance the raw EEG signal against any expected artifacts or noise. Second, the purified EEG signal is decomposed into a number of sub-bands by applying the wavelet transform technique where a number of spectral and statistical features are extracted. Third, the extracted features are examined using the artificial bee colony approach in order to optimally select the best features. Lastly, the selected features are treated using the proposed NEODL classifier, where the input signal is classified according to the problem at hand. The proposed approach is evaluated using two benchmark datasets and addresses two neurological disorder applications: epilepsy disease and motor imagery. Several experiments are conducted where the proposed classifier outperforms other deep learning techniques as well as other existing approaches. The proposed framework, including the proposed classifier (NEODL), has a promising performance in the classification of EEG signals, including epilepsy disease and motor imagery. Based on the given results, it is expected that this approach will also be useful for the identification of the epileptogenic areas in the human brain. Accordingly, it may find application in the neuro-intensive care units, epilepsy monitoring units, and practical brain-computer interface systems in clinics.