When the eyes follow a target that is moving directly towards the head they make a vergence eye movement. Accurate perception of the target's motion requires adequate compensation for the movements of the eyes. The experiments in this paper address the issue of how well the visual system compensates for vergence eye movements when viewing moving targets. We show that there are small but consistent biases across observers: When the eyes follow a target that is moving in depth, it is typically perceived as slower than when the eyes are kept stationary. We also analysed the eye movements that were made by observers. We found that there are considerable differences between observers and between trials, but we did not find evidence that the gains and phase lags of the eye movements were related to psychophysical performance.