Summary I consider the analysis of capture–recapture models with individual covariates that influence detection probability. Bayesian analysis of the joint likelihood is carried out using a flexible data augmentation scheme that facilitates analysis by Markov chain Monte Carlo methods, and a simple and straightforward implementation in freely available software. This approach is applied to a study of meadow voles (Microtus pennsylvanicus) in which auxiliary data on a continuous covariate (body mass) are recorded, and it is thought that detection probability is related to body mass. In a second example, the model is applied to an aerial waterfowl survey in which a double-observer protocol is used. The fundamental unit of observation is the cluster of individual birds, and the size of the cluster (a discrete covariate) is used as a covariate on detection probability.