This chapter begins by presenting the Hidden Markov models (HMM) formulation for standard mark—recapture—recovery (MRR) data without covariate information, and includes individual-specific time-varying continuous covariate information. It illustrates the extension by investigating how the body mass of the Soay sheep affects their probability of survival. MRR data are conveniently expressed as capture histories of the individual animals. For basic MRR data, the likelihood can be calculated more efficiently by using sufficient statistics. The chapter considers the case in which the covariates are individual-specific, time-varying and continuous-valued, for example the condition of the individual as measured by proxies such as body mass or parasitic load. The extension to multiple covariates is straightforward in principle but it involves a large increase in computation time. The survival probability increases with increasing body mass, with this effect strongest for lambs and seniors, and weakest for adults.