The binomial-logit mixed models are generalized linear mixed models for dichotomous or counting variables that take into account the between domains variability, that is not explained through auxiliary variables, by introducing random effects. For fitting the model, this chapter describes the method of simulated moments, the EM and the ML-Laplace approximation algorithms are also introduced. The chapter presents several model-based predictors of population-based and model-based parameters and treats the problem of MSE estimation by parametric bootstrap. The last section provides R codes.