Any malignancy, mainly hematological, may be sensitive (with complete remission) to high-dose chemo and/or radiotherapy. The dose of most antineoplastic agents is limited by the toxicity to the normal marrow. The availability of marrow for transplantation (allogenic, syngenic or autologous), and the capability of reconstituting hematopoietic function, makes it possible to administer chemoradiotherapy in supralethal doses in an effort to kill a greater fraction of the malignant cells. Total Body Irradiation is used both to eradicate the malignant cells and to suppress host immune reactivity enough to prevent rejection of allogenic marrow. The transplanted allogenic marrow can also exert an antitumor effect. A survey of radiobiological studies undertaken is presented and preliminary results of a series of patients treated with TBI at ISSR are discussed.