Different studies have demonstrated that offspring longevity depends on parental longevity and parental age at conception. The present paper suggests, based on the telomere theory of aging, that the longevity of the offspring is proportional to the telomere length and inversely proportional to the telomere state of integrity in the sperm cell and oocyte at conception. These two characteristics of telomeres depend on the age of parents. Telomeres become longer in gametes during the course of life, but at the same time they accumulate mutations (reduced state of integrity) that cause a faster loss of repetitive sequences. Because of these two mechanisms with opposing effects, there could exist an ideal age of the parents for the transmission of maximal longevity. The different longevity of men and women could partly be the result of different telomere dynamics of the sex chromosomes. The hypothesis also explains the risk of some birth defects associated with parental age at birth (telomeres are taken as a cause of birth defects).