In this paper the analysis of models for assessing the migration of ra
dioactive substances from catchments to water bodies was carried out,
Comparisons are made between the mathematical form of the experimental
dissolved radionuclide transfer functions (Transfer Function = the am
ount of radionuclide flowing per unit time from upstream drainage basi
n to a water body following a single-pulse deposition of radioactive s
ubstance) evaluated for rivers in Europe contaminated after the Cherno
byl accident, with the ''Green Functions'' (Green Function = the radio
nuclide now per unit time from catchment to water body calculated by t
he model as a result of a single-pulse input deposition) characterizin
g some of the most common models. Generally transfer functions are the
sum of some time-dependent exponential components. The analysis showe
d that two main components (a short-term and a long-term component) ma
y be detected over a period of only a few years after the accident. Th
e comparison of transfer functions and Green functions showed that a)
models based on the traditional concept of k(d) (the radionuclide part
ition coefficient soil-water) do not explain the higher value of the e
xperimental long-term effective-decay constant for Cs-137 compared wit
h Sr-90; and b) traditional models do not explain the nonlinear depend
ence of the flux (Bq s(-1)) of dissolved Sr-90 migrating through a cat
chment as a function of the water nux, A semi-empirical model was deve
loped to give reason for the above effects, This model is based on phe
nomena of water saturation in different soil layers and on the nonreve
rsible processes responsible for the non-availability to migration of
radionuclides.