  We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2)
symmetric model. We drive the system out of equilibrium by introducing a
non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic
Langevin description of the system, while maintaining the O(2) symmetry of the
order parameter space. By performing dynamic renormalization group calculations
in a field-theoretic set up, we analyze the ensuing nonequilibrium steady
states and evaluate the scaling exponents near the critical point, which now
depend explicitly on $D_\times$. Since the latter remains unrenormalized, we
obtain universality classes varying continuously with $D_\times$. More
interestingly, by changing $D_\times$ continuously from zero, we can make our
system move away from its equilibrium behavior (i.e., when $D_\times=0$)
continuously and incrementally.
