  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.
