Proton beams of the Joint Institute for Nuclear Research (LNP, JINR) Dubna synchrocyclotron and of the proton synchrotron of the Institute for Theoretical and Experimental Physics (ITEP) Moscow have been used for medical and biological purposes since 1967. 58 patients in JINR and 163 in ITEP with various types of malignant tumors have been treated. Results of clinical research showed that use of high energy protons for treatment of malignant tumors is quite expedient and may serve as a good approach developing better means for irradiation in oncological therapy. Proposals for proton and meson beams at the JINR high intensity phasotron and for proton beams at the ITEP medical and biological center are discussed. The ITEP center will consist of 4 cabins for therapy and 2 cabins for radiobiological research, which will permit to treat ~ 100 patients per day.