  This paper deals with the asymptotic statistical properties of a class of
redescending M-estimators in linear models with increasing dimension. This
class is wide enough to include popular high breakdown point estimators such as
S-estimators and MM-estimators, which were not covered by existing results in
the literature. We prove consistency assuming only that $p/n \rightarrow 0$ and
asymptotic normality essentially if $p^{3}/n \rightarrow 0$, where $p$ is the
number of covariates and $n$ is the sample size.
