Growth, digestion, and passage kinetics in ruminants were studied as reference problems of nonlinear phenomena in animal science to be analyzed using nonlinear models. The statistical packages R and SAS were compared in terms of their nonlinear parameter estimation by ordinary nonlinear least squares and maximum likelihood algorithms. The assessed programs included the nls2, nlsLM, and nlme functions of R, and the NLIN, %NLINMIX macro of SAS. The quality of fit of the models was evaluated through likelihood criteria. The NLIN, nls2, and nlsLM functions yielded nonlinear parameter estimates that were almost equal in terms of scale; nevertheless, the interval estimates obtained with nls2 and nlsLM were within those estimated with PROC NLIN, despite the fact that the approximate confidence intervals are estimated using the same Student's t-test in both R and SAS. The degradation of fiber and passage kinetics of particulate markers were predicted with very small numerical differences both in terms of scale and dispersion estimates. For the nonlinear mixed-effects models used to interpret growth data, the nlme (R) and %NLINMIX macro (SAS) algorithms differed in terms of the value of the likelihood function whenever heterogeneous variances, correlations, and weighting variances were fitted; nonetheless, when assuming independence and homoscedasticity, the results of the log-likelihood function were identical. The number of possible models fitted to the growth profiles was 28 with nlme function of R, whereas with %NLINMIX macro of SAS, only 13 possible models were fitted. Fortunately, the conclusions reached by fitting growth models to lamb growth data with either R or SAS were the same. Nonetheless, because each fitting experience is unique, there is no guarantee that the same conclusions would be achieved because the programs do not behave equally in the case of fitting nonlinear mixed models with different correlation and variance structures combinations. Funded by CNPq, CAPES, and FAPERJ.