It is assumed that in the long run U.S. population growth will have to cease, as otherwise life will become physically impossible. Various hypothetical possibilities of achieving such a type of development are investigated. Alternatives of reproduction rate trends are considered in terms of alternatives of interactions of assumed age-specific fertility and mortality trends and these are computed and evaluated. The various computations then indicate the nature of childbearing attitudes and behaviour, which the ‘average population’ would have to adopt in order to achieve the desired stationary population growth after a certain period of time. On the other hand the results presented in the paper also indicate that a certain population growth (of the order of 30–50%) and change in age structure is inevitable in the coming 5–10 decades given the initial childbearing behaviour.