Determination of a groundwater's mean residence time with the aid of environmental tracers is common in hydrogeology. Many of the lumped parameter (LP) applications used for this purpose have been based on steady-state models. However, the results may be misleading if a steady LP model is used to simulate the environmental tracer transport in an unsteady aquifer. To test this hypothesis, the results of steady and unsteady versions of several LP models were evaluated theoretically and in an alpine karst aquifer case by using tritium, oxygen-18 and chlorofluorocarbons (CFCs). The results reveal that the mean residence times obtained may be significantly different between the steady and unsteady versions of the same model. For the karst aquifer investigated, a serially connected exponential and a plug flow model were run under unsteady conditions. It is shown that outflux calibration with an unsteady model provides a firm basis in evaluating the results of models. An outflux-calibrated unsteady model predicted reasonably the observed series of water isotopes. The calibrated model's CFCs output overpredicts the observed concentrations, probably because of the time lag in the unsaturated zone of the alpine karst aquifer. Copyright (c) 2005 John Wiley & Sons, Ltd.