The objective of this project is to advance the mathematical theoretical foundations of pharmacokinetics, particularly in the area of qualitative description of the behavior of incompletely characterized pharmacokinetic systems (e.g., systems in which the number and connections of compartments and the transfer rate coefficients are unknown). It will apply the methods of functional analysis and system theory in order to derive theorems on such subjects as mean drug levels on repetitive dosage schedules, peak drug levels, relative drug levels in different body regions, super-position principles, and optimum dosage schedules. It will also employ a high-speed digital computer for such purposes as simulating examples, providing counterexamples to disprove hypotheses, and finding particular numerical values. Related problems which may be taken up include the theory of dosage schedules in chemotherapy, the convection-diffusion problem, sequential methods for empirical optimization, and the analysis of measurement structures.