In the present paper, a quasilinear model of the rainfall-runoff transfer is developed by means of a regional dimensionless kernel function. The instantaneous unit hydrograph (IUH) for a specific storm on a specific watershed is obtained by rescaling the regional dimensionless kernel by using the peak discharge of the IUH, the time lag of the watershed and storm characteristics. The peak discharge of the IUH and the time lag of the watershed are obtained by the given regression relationships. The model is tested by predicting the direct runoff from an urban watershed, the data from which were not used for the calibration of the model. A nonlinear deterministic model involving two kernel functions is used to compute the direct runoff from the rainfall excess. The first and second-order kernels vary with the number of storms used. The regeneration performance of the nonlinear model was not as good as that of the quasilinear model. The runoff hydrographs are sensitive to errors in the second order kernel function. /Author/