This study presents systems of delayed differential equations which predict serum concentrations of hormones important for regulation of the menstrual cycle. Parameters for the systems are fit to two different data sets for normally cycling women. For these best-fit parameter sets, simulations for the two models agree well with the data but one model also has a stable periodic solution representing an abnormal menstrual cycle. Differences in model behavior are explained by studying hysteresis curves in bifurcation diagrams with respect to sensitive model parameters. For instance, one sensitive parameter is indicative of the estradiol concentration that promotes pituitary synthesis of a large amount of luteinizing hormone, which is required for ovulation. The model may be extended to normally cycling women from age 20 to age 50 by including the pool of primordial follicles that a woman is born with and its natural decline with age. Model simulations show that this decline may be slowed by the administration of exogenous antimüllerian hormone resulting in a delay in the onset of menopause as measured by the number of primordial follicles remaining in the ovaries.