To allow for the identification of genetic differences in preweaning growth among Hereford calves participating in a record of performance program, in the state of Rio Grande do Sul, Brazil, a model should contain, at least, the following environmental explanatory variables: contemporary group classes, age of dam spline-regressors nested in sex of calf, nursing status at last mating season of the dam classes, date of birth of calf spline-regressors nested in calving seasons, and linear and quadratic age of calf regressors;Generalized least squares estimates of the above environmental effects and of sire effects nested in sets were obtained. Restricted maximum likelihood estimates of error and sire variances indicate that selection for weaning weight would respond to selection. To obtain these estimates a combination of the Common Intercept Approach and of Givens rotations was used to perform the iterations and to obtain the converged values in a fast and efficient manner. Robust estimation techniques are discussed and preliminary results show that such techniques could aid in animal selections;Operational methods to optimally solve animal breeding problems characterized by the sequential accumulation of batches of field data are investigated or discussed.