In this work we sttudy some models of tumor growth, which consider the type with necrotic and nonnecrotic core. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symetric, and its boundary is an unknown function r=R(t). The main objective is to achieve an optimal control for our problem. In other words we want to find the best way for the patient to have a longer survival times.