We present multi-epoch 8.4 and 43 GHz Very Long Baseline Array images of the BL Lac object 0735+178. The images confirm the presence of a twisted jet with two sharp apparent bends of 90$^{circ}$ within two milliarcseconds of the core, resembling a helix in projection. The observed twisted geometry could be the result of precession of the jet inlet, but is more likely produced by pressure gradients in the external medium through which the jet propagates. Quasi-stationary components are observed at the locations of the 90$^{circ}$ bends, possibly produced by differential Doppler boosting. Identification of components across epochs, since the earliest VLBI observations of this source in 1979.2, proves difficult due to the sometimes large time gaps between observations. One possible identification suggests the existence of superluminal components following non--ballistic trajectories with velocities up to $11.6pm 0.6 h_{65}^{-1} c$. However, in images obtained after mid-1995, components show a remarkable tendency to cluster near several jet positions, suggesting a different scenario in which components have remained nearly stationary in time at least since mid-1995. Comparison with the earlier published data, covering more than 19 years of observations, suggests a striking qualitative change in the jet trajectory sometime between mid-1992 and mid-1995, with the twisted jet structure with stationary components becoming apparent only at the later epochs. This would require a re-evaluation of the physical parameters estimated for 0735+178, such as the observing viewing angle, the plasma bulk Lorentz factor, and those deduced from these.
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