A non-linear integral model of a one-species population constructed in the paper takes into acccount the dependence of the population fertility and mortality rates on age and intra-species competition. The existence and stability of stationary solutions are analyzed. The model is then extended to the case of two populations with intraand inter-species competition. For the latter model, conditions of the existence of a non-trivial positive stationary solution are obtained and discussed. © Dynamic Publishers, Inc.