Duffy and Wurtz [(1993) Vision Research, 33, 1481-1490] found an illusory shift in the position of the focus of expansion (FOE) of random dot patterns when planar motion was superimposed on expanding radial motion. Subjects indicated that this illusory shift was in the direction of the planar motion. This is the opposite direction to a true shift in the FOE that is perceived when the planar motion is vector summed with the expanding motion. We account for this illusion by suggesting that planar motion induces opposite motion on the expanding dots which after vector summation produces the illusory shift in the FOE. We use a matching technique with a method of adjustment to measure induced motion and perceived FOE in moving random dot patterns and present the results in support of our assertion.