The purpose of this article is to model the progression of CD4-lymphocyte count and the relationship between different features of this progression and survival time. The complicating factors in this analysis are that the CD4-lymphocyte count is observed only at certain fixed times and with a high degree of measurement error, and that the length of the vector of observations is determined, in part, by the length of survival. If probability of death depends on the true, unobserved CD4-lymphocyte count, then the survival process must be modelled. Wu and Carroll (1988, Biometrics 44, 175-188) proposed a random effects model for two-sample longitudinal data in the presence of informative censoring, in which the individual effects included only slopes and intercepts. We propose methods for fitting a broad class of models of this type, in which both the repeated CD4-lymphocyte counts and the survival time are modelled using random effects. These methods permit us to estimate parameters describing the progression of CD4-lymphocyte count as well as the effect of differences in the CD4 trajectory on survival. We apply these methods to results of AIDS clinical trials.