An atmosphere condensing and subliming seasonally about the poles of a a planet loses and gains mass relatively more rapidly than it does angular momentum. An exploratory analysis indicates that a seasonal cycle of mean zonal winds is produced. These exert a seasonally variable torque on the surface of the planet which transfers angular momentum between the atmosphere and the solid planet, inducing seasonal fluctuations in the planet's rotation. The analysis is applied to Mars. It yields seasonal variation in zonal wind direction consonant with that inferred from Viking Orbiter images of south polar regions; and it predicts cumulative seasonal fluctuations in the rotation of Mars of about ¿40 milliseconds. The measurement of such fluctuations appears feasible and would provide an independent source of insight into gross features of Martian meteorology.