For pt.II see ibid., vol.3, p.407-19, (1986). In part I, a model was developed for describing the behaviour of the piezometric head during slug or displacement tests in a well-aquifer system where the well fully penetrates a confined aquifer. Assuming the parameters in the system are known, a theoretical solution was derived. In part II, a numerical procedure which implemented these results was given and in particular it was shown how to calculate the fluctuations in the elevation of the water surface in the well. In this paper, the authors take up the inverse problem of estimating the aquifer transmissivity and storativity from field measurements of the depth of the water surface elevations inside the well. They assume that these measurements have been taken at discrete points in time and then prove the continuous dependence of the aquifer characteristics on the data and the time interval. Furthermore, they present and test a numerical procedure for estimating the aquifer transmissivity and storativity. Although this work focuses on radial flow problems, it is evident that the basic analysis of the procedure applies equally well for any well-aquifer model. A field example illustrating the applicability of the method is presented.