We present observations of the optical "moving lines" in spectra of the Galactic relativistic jet source SS433 spread over a twenty year baseline from 1979 to 1999. The red/blue-shifts of the lines reveal the apparent precession of the jet axis in SS433, and we present a new determination of the precession parameters based on these data. We investigate the amplitude and nature of time-and phase-dependent deviations from the kinematic model for the jet precession, including an upper limit on any precessional period derivative ofṖ < 5 × 10 −5 . We also dicuss the implications of these results for the origins of the relativistic jets in SS433.