  We study the phase-ordering kinetics of the one-dimensional Heisenberg model
with conserved order parameter, by means of scaling arguments and numerical
simulations. We find a rich dynamical pattern with a regime characterized by
two distinct growing lengths. Spins are found to be coplanar over regions of a
typical size $L_V(t)$, while inside these regions smooth rotations associated
to a smaller length $L_C(t)$ are observed. Two different and coexisting
ordering mechanisms are associated to these lengths, leading to different
growth laws $L_V(t)\sim t^{1/3}$ and $L_C(t)\sim t^{1/4}$ violating dynamical
scaling.
