This paper proves the asymptotic normality of estimators which are functionals of the e.d.f. \(\hat F_ n\) such as R, L, M-estimators or minimum distance estimators. Following \textit{J. A. Reeds}' ''On the definition of von Mises functionals.'' Ph. D. Thesis, Havard Univ. (1976), it uses the concept of compact derivative which is intermediate between Gâteaux and Fréchet's definitions. The basic result is the obtention of the compact derivative of the inverse c.d.f. when the range space is \(C^ 0(R)\), with the uniform norm. This provides the asymptotic distribution for a broader class of functionals than previous frameworks. The corollaries for robust estimators are particularly emphasized on L-estimators. Applications are given to one-sample problems, data grouped by quantiles and censored survival data.