Immunotherapy is set as an asymptotic target control problem under mixed state-control constraints with tumor dynamics given by a general ODE. Then a set-valued approach based on Aubin viability theory is used to design feedback protocols with which density of cancer cells may decrease to zero. Existence of such protocols involves a condition C on initial data; otherwise it is shown that either cancer cells cannot be eliminated or condition C may be achieved at a certain instant, in which case the above protocols can then be used. In order to illustrate the approach two examples are studied.