Previously we showed (Wang, Guerra & Cohen 1998) that a statistically robust version of the Haseman & Elston (1972) sib-pair method greatly increased power to detect linkage in the presence of outliers. In this paper we report on M-estimation to accommodate outliers in the variance-components approach to linkage analysis developed by Amos (1994). Simulations show that in the presence of outliers the robust variance-components approach provides substantially greater power, more precise estimation of heritabilities, and better false-positive rates than the original Gaussian based approach. In the absence of outliers the performance of the robust variance-components approach is similar to that of the Gaussian based approach. For illustration we apply the method to two well characterized lipoprotein systems.