We compare and contrast two methods for fitting probability models to data which arise when animals are marked in batches, without individual identification, and live in several different sites or states. The methods are suitable for populations in which animals are marked at birth and then resighted over several sites/states, for small animals going through several growth stages (insects, amphibiae, etc.), as well as for the follow-up of animals released after laboratory colour-marking, for example. The methods we consider include a multi-state model for resightings of batch-marked animals, allowing us to estimate survival, transitions, and sighting probabilities. One method is based on the EM algorithm, and the second uses the Kalman filter for computing likelihoods. The methods are illustrated on real data from a cohort of Great Cormorants Phalacrocorax carbo, and their performance is evaluated using simulation. We recommend identifying the batches, for instance in the case of sites, by using a different colour on each site at the time of marking, and in general the use of the Kalman filter rather than the EM-based approach.