About ten years aga devices and equipment were developed for producing quantitative images in vivo of the distribution of substanees with positron- emitting radionuclide label of very short half-life (down to only several minutes). The positron-emitting isotopes can be the most important bio- elements and are, therefore, suitable for the labeling of important physio- logie substrates like sugars, amino acids ete. and their synthetic analogues. Their imaging, after distribution in vivo, is being performed by PET scan- ning systems. It soon became apparent that positron-emission tomography could be very useful in the field of cancer biology, diagnostics and therapy. Trans- port, influx and efflux, metabolism of suitable labeled substrates around and in tumors can be followed over aperiod oftime, thus allowing the - calization oftumors and - equally important - the efficiency (or non-effi- ciency) of any given therapeutic regimen. For this purpose 13N-Iabeled amino acids, especially glutamate, or l1C_ and 18P-labeled glucose deri- vates were introduced and are already being recommended for the study of special tumors in experimental animals and man, such as brain tumors or osteosarcomas. Some glucose derivatives were developed which differ in their metabolie (enzymatic) fate. In this way, combined application of compounds, like [18F]-2-fluoro-2-deoxy- and rtC]-3-0-methyl-D-glucose are "expected to provide the most important imaging in tumor diagno- stics" (M. Hatanaka). In principle, tlJmor chemotherapy and other therapeutic approaches can now be followed continuously.