Summary: In this paper, we examine the global dynamics of the complete Owen-Sherratt model describing the tumor–macrophage interactions. We show for this dynamics that there is a positively invariant polytope. We give upper and lower ultimate bounds for densities of cell populations involved in this model. Besides, we derive sufficient conditions under which each trajectory in \(\mathbb R^5_+\) tends to the mutant cells-free equilibrium point or to the equilibrium point of macrophages in isolation or to the coordinate plane corresponding to the absence of normal tissue cells depending on initial conditions. The biological sense of our results is discussed as well.