Induced motion is the false impression that physically stationary objects move when in the presence of other objects that really move. In this study, we investigated this motion illusion in the depth dimension. We raised three related questions, as follows: (1) What cues in the stimulus are responsible for this motion illusion in depth? (2) Is the size of this illusion affected by vergence eye movements? And (3) are the effects of eye movements different for motion in depth and for motion in the frontoparallel plane? To answer these questions, we measured the point of subjective stationarity. Observers viewed an inducer target that oscillated in depth and a test target that was located directly above it. The test target moved in phase or out of phase with the inducer, but with a smaller amplitude. Observers had to indicate whether the test target and the inducer target moved in phase or out of phase with one another. They were asked to keep their eyes either on the test target or on the inducer. For motion in depth, created by binocular disparity and retinal size change or by binocular disparity alone, we found that when the eyes followed the inducer, subjective stationarity occurred at approximately 40-45% of the inducer's amplitude. When the eyes were kept fixated on the test target, the bias decreased tenfold to around 4%. When size change was the only cue to motion in depth, there was no illusory motion. When the eyes were kept on an inducer moving in the frontoparallel plane, induced motion was of the same order as for induced motion in depth, namely, approximately 44%. When the induced motion was in the frontoparallel plane, we found that perceived stationarity occurred at approximately 23% of inducer's amplitude when the eyes were kept on the test target.