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A hybrid brain–computer interface (BCI) system that combines a self-paced BCI and an eye-tracker is proposed for text-entry applications. To make a text-entry of a letter/word, the user must gaze at the target for at least a specific period of time (called the dwell time) and then activate the self-paced BCI with an attempted hand extension. Although the self-paced BCI is available for use at any time, a built-in sleep mode is activated when the user is not looking at a letter/word or when the user gazes at a letter/word for less than the dwell time. Such a design has the advantage of greatly minimizing the false positive outcomes compared to the state-of-art self-paced BCIs. To further improve the system's performance, a method that adaptively updates the BCI classifier is also proposed. The results from seven able-bodied individuals show great improvements compared to the pure self-paced BCI. For dwell times of 0.75 and 1.00 s, the number of false-positives/minute is significantly reduced to 2.5 and 1.7, at acceptable average true positive rates of 54.5% and 54.1%, respectively.