The chief aims of this paper were the following: (i) to describe the demography and genetic structure in two divergent selected lines for total fleece weight (TFW) of French Angora rabbits with overlapping generations; (ii) to describe the effects of inbreeding during an experiment of divergent selection. A study of longevity with the survival kit showed that there was no significant difference in the risk of death or culling between the low line (LL) and high line (HL). A significant effect of inbreeding (p < 0.05) was observed with a 30% higher risk factor in the highest class of inbreeding coefficient compared with the other classes. The means of generation interval were 562 and 601 days in LL and HL, respectively. The numbers of generations for LL and HL were 3.90 and 3.64, respectively. Generation intervals decreased significantly from 1995 to 2000 (p < 0.05). The number of daughters in HL was very variable. The number of animals per generation was higher in HL than in LL. Each buck left nearly three daughters to the next generation (2.52 in LL, 3.24 in HL). In both lines, the effective number of ancestor genomes still present in the genetic pool of the generation was around eight from the reference population of 1995 to that of 2001. Inbreeding in HL was always higher than in LL. The effect of inbreeding was also significant (p < 0.05) on TFW and live weight. The animals with the lowest inbreeding category produced a higher TFW (p < 0.05) than the others. The observed selection differentials were lower than that expected owing to the breeding animal management rules in order to control inbreeding increase.