  We investigate nonequilibrium critical properties of $O(n)$-symmetric models
with reversible mode-coupling terms. Specifically, a variant of the model of
Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed
balance is incorporated by allowing the order parameter and the dynamically
coupled conserved quantities to be governed by heat baths of different
temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the
field-theoretic renormalization group are applied to one-loop order, and yield
two new fixed points in addition to the equilibrium ones. The first one
corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical
behavior for the order parameter and to anomalous noise correlations for the
generalized angular momenta; the second one is at $\Theta = 0$ and is
characterized by mean-field behavior of the conserved quantities, by a dynamic
exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by
modified static critical exponents. However, both these new fixed points are
unstable, and upon approaching the critical point detailed balance is restored,
and the equilibrium static and dynamic critical properties are recovered.
