The study presents the results of applying two isolated event, constant runoff proportion, conceptual models to a range of catchments drawn from various climatic and physiographic regions of South Africa and the USA. The models can be operated in either lumped or semi-distributed modes. The research progressed through the following stages. The initial stage involved the calibration of both models on two sets of catchments so that an initial evaluation of the performance of the models could be carried out and any deficiencies in the model structure identified, and where practical, corrected. The models were then calibrated on a further 8 catchments. An important result of the calibration is that for both models to produce reasonably acceptable simulations, at least one parameter has to vary between storms on the same catchment to account for variations in storm or antecedent moisture characteristics. The next stage consisted of compiling quantitative descriptions of the physical characteristics of the catchments and rainfall events and an attempt to relate the calibrated parameter values to relevant physical characteristics for the purpose of estimating parameter values when calibration is not possible. Despite the difficulties encountered in quantifying some of the hydrological characteristics the general trends exhibited by many of the relationships are encouraging and the format of the combinations of physical variables used, do make sense with respect to the original parameter conceptualisations. The relationships between storm characteristics and parameters of both models are less satisfactory. There is a high degree of scatter and the between-catchment variation in the form of the relationships, indicates that the derived relationships are likely to be of little use for parameter estimation purposes. The final stage involved a validation exercise in which new parameters were estimated from the physical variable-parameter relationships for all the catchments previously used, as well as a further four. The new parameters were used to re-simulate all the storms and comparison of these results were made with the original calibration results. Both models produced poor results and are unlikely to give reliable results where calibration is not possible. The parameter relationships for the parameters related to storm characteristics are so catchment specific that transfer to other areas will produce unpredictable results. Foot note:- For compatability with computer printouts decimal full stops are used in the format of real numbers in tables etc