The numerical development of cancer cells during tumor growth and under current forms of therapy is quantitatively described as a fundament of a scientifically founded anticancer strategy. As to general cancer prevention, suppression of metastasis and reduction of recurrencies, figures for orientation are derived, which allow to assess the minimal number of malignant cells to be killed. The killing potency of current tumor immunological measures has been not so far sufficient enough to have a good chance for achieving these pretentious goals. The mean reyason for this to be supposed the neglection of the oxygen status of the body and its dynamics. This is a surprising fact, since all immunological mechanisms are known to be energy-, i.e., oxygen-dependent. The experimentally confirmed correlation between the effectiveness of body defense and the quality of the oxygen status was the origin of several variants of the oxygen multistep immunostimulation concept (application of immunostimulators combined with the oxygen multistep therapy). Clinical results reflect the remarkable increase of the cell-killing potency achievable by these measures and give reasons for the adaptation of anticancer strategies to progress in tumor immunology. Furthermore, real methodological proposals are made for general cancer prevention, suppression of metastasis, and reduction of recurrencies, and the concept of a combined therapy is developed. This therapy comprises the currently accepted measures, such as surgery, irradiation and drugs, and the adjuvant O2 multistep immunostimulation, which is applied three-fold according to a specific schedule. The advantage of this combination is that the patient comes first into the enjoyment of all the beneficial effects that established regimens can offer for the particular case. Then and moreover, the patient gains better quality of life, because the adverse side-effects of radiation and drugs are attenuated and, finally, the individual gets a fair chance of stopping the progression of the disease.