Observations of SS433 are consistent with the view that the Doppler-shifted line emission originates in a pair of oppositely-directed, precessing jets in which a gas outflow is maintained at the remarkably time- and space-invariant speed of 0.26c. A radiative acceleration mechanism is described for the jets and a detailed, numerical, relativistic flow calculation presented which explain this terminal velocity as the result of “line-locking”. The “line-locking” mechanism suggested here for SS433 may be important as well in extra-galactic radio sources in which the radio luminosity is similarly weak compared with the kinetic energy and optical luminosities.