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.