Eye-brain-computer interfaces (EBCIs) could combine the advantages of eye tracking systems used for operating technical devices and brain-computer interfaces. Such systems are intended for both patients with various motor impairments and healthy individuals. The effectiveness of EBCIs is largely dependent on their ability to detect the user’s intent to give a command on the encephalogram (EEG) recorded during gaze fixation, that is, just within hundreds of milliseconds. These strict requirements necessitate a full use of data contained in EEG for more accurate classification of gaze fixations as spontaneous and “control”. This work describes our attempt to use for classification not only amplitude statistical features, but also wavelet features specific to oscillatory EEG components within the interval of 50-500 ms from gaze fixation onset. Integral index of classification accuracy AUC significantly depended on the feature set, reaching the highest value (0.75, average over the group of 8 participants) for the combined amplitude and wavelet set. We believe that further improvement of this method will facilitate the practical application of EBCIs.