In naturally reproducing populations one usually encounters an aver­age number of more than one offspring per individual. However, given non-extinction, classical super-critical branching processes grow beyond all bounds. This is unrealistic because of bounded resources. We consider a model for a population with subpopulations living in separated regions and with migration between the regions. In addition to the births and deaths in a super-critical branching mecha­nism, there are deaths resulting from competition between any two individuals in one subpopulation. We prove that there is...