Recently Lin & Wei (2003) developed the score test for heteroscedasticity in nonlinear regression models and investigated the power of this test through Monte Carlo simulations. This paper presents an approach for estimating local power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The analogous discussion is also given for nonlinear models with random walk errors (ARIMA(0,1,0) errors). The methods are applied to the problem of local power calculations for the score tests of heteroscedasticity in European rabbit data (Ratkowsky, 1983). Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a range of parameter configurations.