We study the early stages of spinodal decomposition (SD) in polymer-liquid-
crystal mixtures by solving linearized time-dependent Landau-Ginzburg equat
ions for concentration (conserved order parameter) and orientation (noncons
erved order parameter). The theory takes into account a cross term between
concentration and orientation gradients, which becomes an important factor
for phase separation kinetics. We calculate structure factors for concentra
tion and for orientation, depending on a quench temperature and concentrati
on. We find a new SD process driven by instability of the orientational ord
er parameter. In this case, the average domain size initially grows as a no
ntrivial and evolving power of time, which starts as t(1/3) in our minimal
model. The domain growth is advanced by the coupling between the two order
parameters.