In this paper we consider several estimators for the variogram: the classical estimator due to Matheron, a robust estimator proposed by Cressie & Hawkins, and two highly robust estimators introduced by Rousseeuw in the context of scale estimation. It will be shown by simulations that the robust estimators behave quite well in the case of dependent data. Several types of dependency structure are studied and the various estimators are also applied to a typical real world example