The use of derivative-free methods to give maximum likelihood estimates of bivariate variance parameters is illustrated. An algorithm is given for the case when the same fixed effect model applies to both traits and the variance matrices for the two traits and the covariance matrix between the two traits have the same structure. Each of these three matrices depending on two variance parameters, giving a total of six parameters. By reparameterising in terms of canonical heritabilities and a transformation matrix a six dimensional problem is reduced to a two-dimensional problem. Extensions to other models are briefly indicated. One important case is when each animal is measured on only one trait

%V XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation. %P 496–499 %G eng