This paper presents a new class of noninvasive brain-computer interfaces based on user’s silent counting of homogeneous visual stimuli, without defining separate classes of target and non-target stimuli (the “single-stimulus” paradigm), at an average (asynchronous) rate of about 2 stimuli per second and with counting that started immediately after moving the gaze to the stimulus presentation area. Interface’s operation was modeled by applying a linear classifier to EEG signals obtained from healthy participants, in rest condition and after moving their gaze to the stimulus presentation position. A response time of 2 second after the beginning of saccade was demonstrated, which is exceptionally fast comparing to typical results known for the existing noninvasive brain-computer interfaces. This result creates a basis for the development of efficient hybrid eye-brain-computer interfaces, considering that integration of the proposed EEG-based interfaces with the analysis of visual fixations and saccades can further improve recognition of the user’s intentional commands.