  We study dynamic field theories for nonconserving $N$-vector models that are
subject to spatial-anisotropic bias perturbations. We first investigate the
conditions under which these field theories can have a single length scale.
When N=2 or $N \ge 4$, it turns out that there are no such field theories, and,
hence, the corresponding models are pushed by the bias into the Ising class. We
further construct nontrivial field theories for N=3 case with certain bias
perturbations and analyze the renormalization-group flow equations. We find
that the three-component systems can exhibit rich critical behavior belonging
to two different universality classes.
