Physical as well as biochemical processes have a significant influence on the material balance of a lake. Mathematical concepts are developed to treat transport phenomena with which a comparison of different lakes under certain systematic aspects becomes possible. A two-box model consisting of the subsystems epilimnion and hypolimnion, for lakes with one specific limiting nutrient factor (e.g., phosphorus) is employed to evaluate eutrophication processes. In particular, a theoretical basis for Vollenweider's  empirical relation between specific phosphorus loading and the trophic state is presented. Finally, the inhomogeneous O2-consumption in the deep part of the lake during summer stagnation is calculated with diffusion theory.