An investigation carried out into the values of lag time for catchment areas as measured from centre of mass of excess rainfall to centre of mass of resulting runoff. Since any variation of this value for an individual catchment is an indication of non-linear response, this study is closely associated with non-linearity of catchment systems. Values of lag were measured for a range of floods on five separate catchment areas and were correlated with a number of factors. The difference in value between catchments was found to be a function of the catchment characteristics, while variations in the value for an individual catchment were strongly related to the magnitude of the floods. As the degree of variation was fairly constant for the areas studiesd, the degree of non-linearity was also considered to differ little between the catchments. Three general formulae have been developed for estimating the lag time of natural catchments: suggestions made regarding their use and estimates of their probable accuracy .Development of the formulae required a detailed analysis of a large volume of hydrological data. An objective systematic procedure was developed to deal with this problem and to carry out the initial correlation studies. For this purpose, lag was measured to the centre of mass of direct runoff, and a novel measure of flood magnitude was devised, viz. weighted mean discharge. Numerous hyetograph characteristics were measured and studied, but none appeared to have any significant influence on the value of lag time. Many incidental conclusions are drawn in regard to various aspects of the work, and several topics suggested for future consideration.