Lange, Westlake & Spence (1976) used the assumption of multivariate normality to apply a likelihood method to the analysis of quantitative traits measured over pedigrees. We now introduce a test of the assumption of multivariate normality and methods for the detection of outlying families and outlying individuals. We also introduce a method for the estimation of effects of measured genetic markers as variance components, a flexible parameterization to estimate effects of shared family environment, and a method to allow for the ascertainment of pedigrees through probands. These innovations have been applied using numerical methods for maximization of the likelihood. Simulation studies and available theory suggest that the likelihood ratio criterion used in significance testing follows the expected asymptotic distribution with sample sizes encountered in typical applications.