The role of the 200 yr-long period found recently in the mean longitude of Mimas (Vienne and Duriez 1992) is investigated through numerical integrations. It is shown that it has a deciding effect on the descriptions of the resonance motion of the Mimas-Tethys system, as considered up to now. As a result, Mimas’s inclination before capture may have been higher (up to 0.7°) or lower (down to 0.03°) than the value previously considered (0.42°). Also, Tethys’s eccentricity on capture may have been quite higher (≈ 0.008 versus 0). Moreover, the probability of capture is found to be very sensitive to Tethys’s eccentricity, and possibly much higher (up to 1) than the value considered before (0.04).