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 of \dot { P } < 5 \times 10 ^ { -5 } . We also dicuss the implications of these results for the origins of the relativistic jets in SS433 .