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 .