The dynamic properties of quadrupolar glasses are investigated on the
basis of a soft-spin version of the recently introduced symmetry adapt
ed random-bond-random-field model. The model is applicable to the mixe
d alkali cyanides and related cubic systems with [100], [111], and [11
0] equilibrium orientations of the quadrupolar axis. Following the dyn
amic theories of Ising and vector spin glasses, a field-theoretic appr
oach is formulated based on the Langevin equation of motion for the sy
mmetry adapted order parameter fields. It is shown that the average re
laxation time diverges on the line of instability T-f(h(r)), where T-f
is the freezing temperature and h(r) the strength of the static rando
m strain fields, in agreement with the static replica theory. For the
[111] model the long-time correlation function exponent nu is evaluate
d along the instability line.