Medical laboratory data are often censored, due to limitations of the measuring technology. For pharmacokinetics measurements and dilution-based assays, for example, there is a lower quantification limit, which depends on the type of assay used. The concentration of HIV particles in the plasma is subject to both lower and upper quantification limit. Linear and nonlinear mixed effects models, which are often used in these types of medical applications, need to be able to deal with such data issues. In this paper we discuss a hybrid Monte Carlo and numerical integration EM algorithm for computing the maximum likelihood estimates for linear and non-linear mixed models with censored data. Our implementation uses an efficient block-sampling scheme, automated monitoring of convergence, and dimension reduction based on the QR decomposition. For clusters with up to two censored observations numerical integration is used instead of Monte Carlo simulation. These improvements lead to a several-fold reduction in computation time. We illustrate the algorithm using data from an HIV/AIDS trial. The Monte Carlo EM is evaluated and compared with existing methods via a simulation study. (C) 2006 Elsevier B.V. All rights reserved..