We propose two sets of tests for structural change in dynamic nonparametric regression models. The first test is based upon sequential kernel estimation of the regression function and thus termed a kernel test. The second test is a CUSUM test based on the cumulative sums of weighted residuals from a single nonparametric regression. We derive the limiting distributions for both tests, and show that they are free of nuisance parameters under the null and have different local power properties. These tests complement conventional parameter instability tests in parametric models. Simulation experiments are conducted to investigate the finite sample properties of these tests. The tests can be used to study many time series where structural changes may occur due to social, economic or financial reform and event .