An increasing number of researchers record binocular eye-tracking signals from participants viewing moving stimuli, but the majority of event-detection algorithms are monocular and do not consider smooth pursuit movements. The purposes of the present study are to develop an algorithm that discriminates between fixations and smooth pursuit movements in binocular eye-tracking signals and to evaluate its performance using an automated video-based strategy. The proposed algorithm uses a clustering approach that takes both spatial and temporal aspects of the binocular eye-tracking signal into account, and is evaluated using a novel video-based evaluation strategy based on automatically detected moving objects in the video stimuli. The binocular algorithm detects 98% of fixations in image stimuli compared to 95% when only one eye is used, while for video stimuli, both the binocular and monocular algorithms detect around 40% of smooth pursuit movements. The present article shows that using binocular information for discrimination of fixations and smooth pursuit movements is advantageous in static stimuli, without impairing the algorithm's ability to detect smooth pursuit movements in video and moving-dot stimuli. With an automated evaluation strategy, time-consuming manual annotations are avoided and a larger amount of data can be used in the evaluation process.