Heteroscedastic data arise in many applications. In a heteroscedastic regression model, the variance is often taken as a parametric function of the covariate or the regression mean. This paper presents a kernel-smoothing based nonparametric test for checking the adequacy of such a postulated variance structure. The test does not need to specify a parametric distribution for the random errors. It has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives. Numerical simulations and an illustrative example are provided
