Abstract: In this article, the population-size-dependent bisexual Galton-Watson
processes are considered. Under some suitable conditions on the mating functions and the offspring distribution, existence of the limit of mean growth rate per mating unit is proved. And based on the limit, a criterion to
identify whether the process admits ultimate extinct with probability one is obtained.

Key words: Bisexual Galton-Watson branching processes, population-size-dependent branching processes, extinction probability