The use of the transfer function F( p), based on the Laplace transformation, in the analysis of residence time distribution curves is considered. It is applied to the two point measuring technique and it is shown that for a low τ p (τ mean residence time between measuring points, p Laplace operator) all models give the same F( p). For flow through packed beds, τ p is recommended to be within a restricted range of 2·0–5·0 to give consistent results of the dispersion parameters. The effect of random fluctuations in the response curves is such that smoothing them is also necessary particularly for radioactive tracer responses.