Abstract: The problem of the competition between tumor cells and immune system, discussed in a previous paper in terms of Lotka-Volterra type interactions, is examined starting from equations for the evolution of dominance in populations of interacting organisms. The saturation effects in the capability of the immune system to destroy the tumor are taken into account, on the basis of two different models proposed in the literature ("Holling model" and "Ivlev model"). In both cases, we deal with a closed set of macroscopic equations, which is examined in the frame of the theory of dynamical systems. Situations leading to depletion of the tumor are studied, comparing the results of the different models, also on the basis of numerical experiments.