Summary: The interest for nonlinear mixed-effects models comes from application areas as pharmacokinetics, growth curves and HIV viral dynamics. However, the modeling procedure usually leads to many difficulties, as the inclusion of random effects, the estimation process and the model sensitivity to atypical or nonnormal data. The scale mixture of normal distributions include heavy-tailed models, as the Student-\(t\), slash and contaminated normal distributions, and provide competitive alternatives to the usual models, enabling the obtention of robust estimates against outlying observations. Our proposal is to compare two estimation methods in nonlinear mixed-effects models where the random components follow a multivariate scale mixture of normal distributions. For this purpose, a Monte Carlo expectation-maximization algorithm (MCEM) and an efficient likelihood-based approximate method are developed. Results show that the approximate method is much faster and enables a fairly efficient likelihood maximization, although a slightly larger bias may be produced, especially for the fixed-effects parameters. A discussion on the robustness aspects of the proposed models are also provided. Two real nonlinear applications are discussed and a brief simulation study is presented.