In the adult murine brain neural stem cells (NSC) are located in the hippocampus and in the subventricular zone. Experiments indicate that the total number of NSC and the number of actively dividing NSC decline with age. However, the decline saturates at old ages and complete extinction of NSC is prevented. Ordinary differential equation models allow to study the mechanisms underlying these changes. The models suggest that an age-related reduction of the rates at which quiescent cells are activated can explain the observed changes. Changes of cell-cycle duration or self-renewal are not in line with the measured dynamics.