The first of a series of papers discussing the qualitative and quantitative aspects of chemotherapy, the treatment of disease through the use of chemical reagents that kill specific types of cells while leaving the patient relatively unpoisoned. Specifically, the series deals with the distribution of a compound in the organs of the body after its injection into the blood stream. The present study considers several simplified mathematical models in which the heart pumps blood to just one organ. It is hoped ultimately to find the characteristics of the most efficacious drugs to use and the manner of their injection. A discussion of models designed to study concentrations of a reagent injected into the blood stream of a relatively simple system consisting of the heart and one organ. Even at this level, there are formidable mathematical problems involving systems of linear and nonlinear parabolic differential equations with time lags in the boundary condition. 27 pp.