The near point of convergence test is widely used to evaluate binocular vision. It assesses the ability of the eyes to converge at short distances. Although the test consists of a pure symmetrical vergence task, small involuntary saccades occur concurrently. The main goal of this study was to analyze saccadic characteristics as a function of vergence demand when testing the near point of convergence. To this purpose, the eye movements of 11 participants were registered with an eye-tracker while they performed the near point of convergence test by following a target that traveled forward and backward on a motorized bench. Saccade amplitude increased and, on average, saccade rate decreased with vergence demand. In general, the direction of the concurrent vergence movement had no significant effect on saccade characteristics. However, each individual subject showed idiosyncratic behavior. Most saccades tended to be corrective in terms of both binocular disparity and individual fixation position errors. In particular, most participants tended to correct the fixation position error of the dominant eye.