A detailed study on the optimisation of the parameter values of the Boughton daily rainfall-runoff model. Optimum values were sought using the Steepest descent, Simplex and Davidson optimising methods. It had been intended to correlate these optimum parameter values with measurable catchment characteristics. Rapid initial reductions in the values of the objective function were readily achieved and the solutions approached apparent optimum points on the response surface. However several of these points were found for each catchment and there were large differences in the parameter values between points. It was found that further improvements in the objective function could usually be achieved by using another of the search techniques or by numerical trials, and in this way, downhill paths on the response surface were found from the apparently optimum points. This work was pursued for one of the catchments until the paths appeared to be converging, but coincidence at a true optimum could not be achieved.. A number of somewhat different sets of parameter values which appeared to lie in a flat "valley" area of the response service were obtained, and these sets gave equally good fits to the observed runoff data. An algebriac analysis of the of the operation of the model and of the effect on the objective function of changes in some individual parameter values led to important findings on some of the problems encountered. It is probable that the findings from the algebriac and numerical analyses would be applicable to the rainfall-runoff models.