A total of 2 946 847 records of up to nine sequential weights of 812 393 Nellore cattle, measured at ages ranging from birth to 733 days, were employed in the present study. Variance components were estimated using a sample data by a 5-trait multiple trait model (MTM), and by a random regression model (RRM) with cubic Legendre polynomials for all random and fixed effects. Expected progeny differences (EPDs) were obtained iteratively by preconditioned-conjugate gradient iteration on data. Accurate solutions with RRM were not obtained until the random regressions were orthogonalized. Correlations between EPDs from RRM and MTM for selected weights ranged between 0.83-0.89. Low correlations were a result of differences in parameters. The findings suggest that estimates of EPDs by RRM may be more accurate than by MTM only if accurate parameters for RRM are available.