Pursuit eye movements give rise to retinal motion. To judge stimulus motion relative to the head, the visual system must correct for the eye movement by using an extraretinal, eye-velocity signal. Such correction is important in a variety of motion estimation tasks including judgments of object motion relative to the head and judgments of self-motion direction from optic flow. The Filehne illusion (where a stationary object appears to move opposite to the pursuit) results from a mismatch between retinal and extraretinal speed estimates. A mismatch in timing could also exist. Speed and timing errors were investigated using sinusoidal pursuit eye movements. We describe a new illusion--the slalom illusion--in which the perceived direction of self-motion oscillates left and right when the eyes move sinusoidally. A linear model is presented that determines the gain ratio and phase difference of extraretinal and retinal signals accompanying the Filehne and slalom illusions. The speed mismatch and timing differences were measured in the Filehne and self-motion situations using a motion-nulling procedure. Timing errors were very small for the Filehne and slalom illusions. However, the ratios of extraretinal to retinal gain were consistently less than 1, so both illusions are the consequence of a mismatch between estimates of retinal and extraretinal speed. The relevance of the results for recovering the direction of self-motion during pursuit eye movements is discussed.