  This paper deals with the Fisher-consistency, weak continuity and
differentiability of estimating functionals corresponding to a class of both
linear and nonlinear regression high breakdown M estimates, which includes S
and MM estimates. A restricted type of differentiability, called weak
differentiability, is defined, which suffices to prove the asymptotic normality
of estimates based on the functionals. This approach allows to prove the
consistency, asymptotic normality and qualitative robustness of M estimates
under more general conditions than those required in standard approaches. In
particular, we prove that regression MM-estimates are asymptotically normal
when the observations are $\phi$-mixing.
