This paper describes, from a mathematical viewpoint, the cellular changes in the granulosa of ovarian follicles during their terminal development. A dynamic model takes into account the processes of (1) cell division, (2) exit from the cell cycle towards differentiation, and (3) apoptotic cell death. Proliferative cells leave the cycle in an irreversible way. The risk of entering apoptosis applies to non-cycling cells. Changes in the cell numbers and in the growth fraction are derived from differential equations. The transitions between the different cell states are ruled by time-dependent rates. Numerical applications of the model concern ovulating and degenerating ovarian follicles in the ewe. The main feature of the ovulating case is the progressive exhaustion of the proliferating compartment for the benefit of the non-cycling cells. From an initial mainly proliferative state the granulosa progressively switches to a highly differentiated state, so that the growth fraction continuously decreases. In the atretic cases, the pattern of changes in the total viable cell number is influenced by the follicular age at the onset of the apoptotic process and by the intensity of the cell death rate. As apoptosis affects the non-cycling cells, the growth fraction is no longer strictly decreasing. The sensitivity of the model to the parameters is studied in a more general framework than the granulosa cell population.