We propose a procedure for maximum likelihood estimation of the number of a
nimals or offspring in a closed population where the individuals counted go
through stages or age-groups. Application of the procedure requires knowle
dge of the distributions of the stage durations. A procedure for maximum li
kelihood estimation of those based on marked animals is also given. The pro
cedures are illustrated by applying them to gray seal (Halichoerus grypus)
data from Froan Nature Reserve, Central Norway, from the breeding seasons 1
990-1999.