This issue of the BELLE Newsletter is designed to address the development of biologically based modeling that may be useful in explaining U-shaped dose-response relationships to carcinogen related responses. The three dose-response relationships selected for analysis are well known in the toxicological and/or epidemiological literature and include the following: dioxin (TCDD-induced liver foci and tumors; saccharin induced urinary bladder hyperplasia and tumors; and radon induced lung tumors. The BELLE Office invited individuals who have made significant contributions in each area to present their scientific explanation to account for the biological basis of the reported U-shaped responses (Dr. Melvin Andersen, ICF Kaiser for TCDD; Dr. Kenneth Bogen, Lawrence Livermore National Laboratory for radon; and Dr. Thomas Downs, University of Texas for saccharin). Each invited expert was to provide a limited, broadly readable summary, interpretation and perspective of approximately 3,000 words each. Then each author was permitted the opportunity to provide comment on the other two modelling approaches. Three outside experts (Dr. David G. Hoel, Medical University of South Carolina, Dr. Suresh Moolgavkar, Fred Hutchinson Cancer Research Center, and Dr. Christopher Portier, National Institute of Environmental Health Sciences) were invited to comment/critique on the papers of Drs. Andersen, Bogen, and Downs. Finally, Drs. Andersen, Bogen, and Downs were allowed a final response to the above comments. We trust that you will find this issue of the BELLE Newsletter an intriguing and unique attempt to explore the concept of U-shaped dose responses for carcinogens and to appreciate the thoughtful views some of the leading scientists in this area. The readership is strongly invited to offer for debate and/or comment their own responses to this issue. Any such comments should be sent to the BELLE Office. Such responses will be considered for publication in the BELLE Newsletter and/or the BELLE Website.