more characteristic lengths, with laws that, besides the specific mechanisms discussed above, depend on the conservation laws of the dynamics.

Generally, the late stage is characterized by dynamical scaling. This implies that a single characteristic length $L(t)$ can be associated to the development of order in such a way that configurations of the system are statistically independent of time when lengths are measured in units of $L(t)$. The characteristic length usually has a power law growth $L(t)\propto t^{1/z}$. In systems with a non-conserved order parameter one generally finds $z=2$. In particular, this value is provided by the exact solution of the kinetic Ising chain [@Glauber63] quenched to zero temperature.

However, there are cases where dynamical scaling is violated, notably the XY model in $d=1,2$. In $d=1$ this is related [@Rutenberg95] to the presence of two lengths $L_w(t)$ and $L_c(t)$, associated to the texture length and to the texture-antitexture distance, growing with different exponents $z=4$ and $z=2$ respectively.

In this Article, we investigate the interplay between two coarsening mechanisms, point-like defect annihilation and texture growth, in the phase-ordering kinetics of the one dimensional $p$-state clock model. This spin system reduces to the Ising model for $p=2$ and to the XY model 