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We propose a procedure for maximum likelihood estimation of the number of animals or offspring in a closed population where the individuals counted go through stages or age-groups. Application of the procedure requires knowledge of the distributions of the stage durations. A procedure for maximum likelihood estimation of those based on marked animals is also given. The procedures are illustrated by applying them to gray seal (Halichoerus grypus) data from Froan Nature Reserve, Central Norway, from the breeding seasons 1990-1999.