In this work, a model of the competition between groups of autonomous agents is constructed and studied. The model assumes that two groups of agents “live” in a one-dimensional cellular world. Agents can distinguish agents of their group from agents of another group, namely, they can distinguish “our agents” from “foreign agents”. Each group is in its own part of the world, in its area. Agents of each group compete for the territory, namely, they patrol their part of the world and strive to expand their part, their area. Agents of a certain group can attack foreign agents and even kill foreign agents. When patrolling, a patrol leader is selected in each group. The leader gives commands to agents of its group to move to the border between areas and attack foreign agents. The model was studied using computer simulation.