Abstract: The assumption of homoscedasticity is a commonly concerned problem in regression analysis. Cook and Weisherg （1983） provided a diagnostic test for heteroscedasticity based on the score statistic in linear regression. In this paper, we extend their result to nonlinear regression . We also obtain a modified score statistic based on the method of Cox and Reid （1987） in which the orthogonality between parameters of interest and nuisance parameters is used. Furthermore,we study the local influence of small perturbations on the score statistic and corresponding diagnostic measures are presented. A numerical example is given to illustrate our results.