The rate of ageing is a genetically influenced feature of an individual's life history that responds to selection on lifespan. Various costs presumably constrain the evolution of prolonged life, but these have not been well characterized and their general nature is unclear. The analyses presented here demonstrate a correlation among birds and mammals between rates of embryonic growth and ageing-related mortality, which are quantified by the exponents of fitted power functions. This relationship suggests that rapid early development leads to accelerated ageing, presumably by influencing some aspect of the quality of the adult individual. Although the mechanisms linking embryo growth rate and ageing are not known, a simple model of life-history optimization shows that the benefits of longer life can be balanced by connected costs of extended development.