Mathematical models in tracer kinetics are usually based on ordinary differential equations which correspond to a system of kinetically homogeneous compartments (standard compartments). A generalization is possible by the admission of inhomogeneities in the behaviour of the elements belonging to a compartment. The important special case of the age-dependence of elimination rates is treated in its deterministic version. It leads to partial differential equations (i.e., systems with distributed coefficients) with the “age” or the “residence time” of an element of the compartment as a variable additional to “time”. The basic equations for one generalized compartment and for systems of such compartments are given together with their general solutions.