  The dynamics of phase-separation in conserved systems with an O(N) continuous
symmetry is investigated in the presence of an order parameter dependent
mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework
of the large-N approximation and by numerical simulations of the N=2, N=3 and
N=4 cases in d=2, for both critical and off-critical quenches. We show the
existence of a new universality class for a=1 characterized by a growth law of
the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the
usual value z=4 which is recovered for a<1.
