Continuous flow vessels which are subject to variation of flow and volume are characterized by time-variable parameters. It is shown that their residence time distributions and weighting functions obtained by tracer testing are made invariant with regard to the integrated flow variables which are introduced. Under variable flow but constant volume, one such integrated variable is sufficient. Under variable volume, two different variables are suggested for the residence time distribution and weighting function, while the appropriate variable of the perfect mixer differs distinctly from that of vessels with a distinct velocity profile. It is shown through a number of example cases, that an agreement with their mathematical models is reached. The approach is extended to include also arbitrary, non-analytic response functions obtained by tracer measurements. Applications of the derived models and their incorporation in automatic control algorithms is discussed.