The Cormack-Jolly-Seber model provides the basic framework for analyzing the survival of animals in open populations using capture-recapture data. Extensions of this model have already been developed that allow the survival and capture probabilities to vary between individuals based on auxiliary variables, but none can allow for variables that are continuous, time-dependent, and vary among individuals. We summarize a new method for incorporating this type of variable into the Cormack-Jolly-Seber model by modelling the distribution of the unobserved values of the variable conditional on the observed values, given a few basic assumptions about how the variable changes over time. We begin with a hypothetical scenario as motivation for our model and also present the results of two examples used in developing the model.