Linear and nonlinear mixed-effects models are widely used in agricultural statistics for analyzing data with complex structures. Recent computational advances have made it easier to estimate parameters in general linear mixed-effects models using methods like maximum likelihood (ML) or restricted maximum likelihood (REML). Software such as SAS PROC MIXED allows analysis of data from random-effects one-way classifications, blocked designs, hierarchical designs, and repeated measures or longitudinal data. These methods do not require balanced data, making them suitable for observational studies and experiments with missing data. The paper describes new computational approaches for fitting mixed-effects models, particularly in the nlme3.0 library for the S-PLUS language. It highlights the use of trellis graphics for data exploration, model fitting, and assessment. For example, trellis plots help visualize grouped data, such as growth curves for baby chicks or blood pressure responses to drug doses. These graphical methods complement traditional statistical analysis techniques. The Laird-Ware formulation is used to describe linear mixed-effects models, and computational methods for estimating maximum likelihood (ML) or restricted maximum likelihood (REML) estimates are discussed. Extensions to nonlinear mixed-effects models are also presented, where random coefficient models are generalized to fit nonlinear data. The paper illustrates how nonlinear mixed-effects models can be applied to soybean growth data, where a logistic growth function is used to model leaf weight over time. The model incorporates random effects for parameters like asymptotic leaf weight, and fixed effects for factors like year and variety. The paper also discusses the importance of graphical methods in model validation, such as residual plots to detect heteroscedasticity. It shows how the variance of the within-group noise term can be modeled as a power of the fitted response, improving the fit of the model. The final model incorporates fixed effects for year, variety, and their interaction, while only a random effect for asymptotic leaf weight is needed. The results demonstrate that incorporating these effects improves the accuracy of parameter estimates and reduces the need for multiple random effects. In summary, linear and nonlinear mixed-effects models provide a flexible framework for analyzing complex data structures in agriculture. Efficient computational methods and graphical tools enable the analysis of data with random effects, repeated measures, and hierarchical designs. These models allow for more accurate parameter estimation and better understanding of within-subject variability.Linear and nonlinear mixed-effects models are widely used in agricultural statistics for analyzing data with complex structures. Recent computational advances have made it easier to estimate parameters in general linear mixed-effects models using methods like maximum likelihood (ML) or restricted maximum likelihood (REML). Software such as SAS PROC MIXED allows analysis of data from random-effects one-way classifications, blocked designs, hierarchical designs, and repeated measures or longitudinal data. These methods do not require balanced data, making them suitable for observational studies and experiments with missing data. The paper describes new computational approaches for fitting mixed-effects models, particularly in the nlme3.0 library for the S-PLUS language. It highlights the use of trellis graphics for data exploration, model fitting, and assessment. For example, trellis plots help visualize grouped data, such as growth curves for baby chicks or blood pressure responses to drug doses. These graphical methods complement traditional statistical analysis techniques. The Laird-Ware formulation is used to describe linear mixed-effects models, and computational methods for estimating maximum likelihood (ML) or restricted maximum likelihood (REML) estimates are discussed. Extensions to nonlinear mixed-effects models are also presented, where random coefficient models are generalized to fit nonlinear data. The paper illustrates how nonlinear mixed-effects models can be applied to soybean growth data, where a logistic growth function is used to model leaf weight over time. The model incorporates random effects for parameters like asymptotic leaf weight, and fixed effects for factors like year and variety. The paper also discusses the importance of graphical methods in model validation, such as residual plots to detect heteroscedasticity. It shows how the variance of the within-group noise term can be modeled as a power of the fitted response, improving the fit of the model. The final model incorporates fixed effects for year, variety, and their interaction, while only a random effect for asymptotic leaf weight is needed. The results demonstrate that incorporating these effects improves the accuracy of parameter estimates and reduces the need for multiple random effects. In summary, linear and nonlinear mixed-effects models provide a flexible framework for analyzing complex data structures in agriculture. Efficient computational methods and graphical tools enable the analysis of data with random effects, repeated measures, and hierarchical designs. These models allow for more accurate parameter estimation and better understanding of within-subject variability.