The effect of variable composition of water and suspended solids in a small river on the kinetics of uptake of58Co and137Cs by the solids has been analyzed using two kinetic models describing the uptake by two consecutive or parallel reactions. At first, experimental data on the kinetics were obtained by laboratory batch experiments with 6 samples of unfiltered water taken under different flow conditions. Then, parameters of the kinetic models were determined by computer fitting of the experimental data. After subtracting the effect of the concentration of the solids, the variability of the parameters due to the variable composition was determined. The results proved that despite the variability, the description of the kinetics by the two-step kinetic models is more accurate than that using a one-step kinetic model. Approximately equal accuracy of the description with both two-step kinetic models was ascertained. It is recommended that kinetic and equilibrium parameters of radionuclide uptake by suspended solids should always be determined by experiments with repeatedly sampled unfiltered water.