A general multinomial modelling approach is proposed for capture-mark- recapture data from an open animal population. Within this framework a number of plausible alternative assumptions are suggested for survival probabilities, ingress times, and capture probabilities. The probability of survival can be time-specific, age-specific, or constant; the distribution of ingress times to the population can be time-specific mixed-uniform, or a beta distribution; and the probability of capture can be time-specific or constant. Taking survival probabilities, ingress times, and capture probabilities as time-specific allows explicit estimators of parameters to be derived. These are identical to the well-known Jolly-Seber estimators, provided that animals are assumed to enter the population in batches just before sample times. However, some differences from the Jolly-Seber estimators occur if it is assumed that entries can take place at any time between samples, for then the models of the pesent paper do not ignore animals that enter and leave the population before a sample is taken. For models with fewer parameters than the Jolly-Seber model, estimation has to be done numerically. The different modelling possibilities are illustrated by the analysis of five sets of real data.