  We present the results of a program to monitor the structure of the radio
emission in 42 $\gamma$-ray bright blazars (31 quasars and 11 BL Lac objects)
with the VLBA at 43, 22, and occasionally 15 and 8.4 GHz, over the period from
November 1993 to July 1997. We determine proper motions in 33 sources and find
that the apparent superluminal motions in $\gamma$-ray sources are much faster
than for the general population of bright compact radio sources. This follows
the strong dependence of the $\gamma$-ray flux on the level of relativistic
beaming for both external-radiation Compton and synchrotron self-Compton
emission. There is a positive correlation (correlation coefficient $r$=0.45)
between the flux density of the VLBI core and the $\gamma$-ray flux and a
moderate correlation (partial correlation coefficient $r$=0.31) between
$\gamma$-ray apparent luminosity and superluminal velocities of jet components,
as expected if the $\gamma$-ray emission originates in a very compact region of
the relativistic jet and is highly beamed. In 43% of the sources the jet bends
by more than 20$^\circ$ on parsec scales, which is consistent with
amplification by projection effects of modest actual changes in position angle.
  In 27 of the sources in the sample there is at least one non-core component
that appears to be stationary during our observations. Different
characteristics of stationary features close to and farther from the core lead
us to suggest two different classes of stationary components: those within
about 2 milliarcseconds (mas) of the core, probably associated with standing
hydrodynamical compressions, and those farther down the jet, which tend to be
associated with bends in the jet.
