We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the regression function or in the conditional variance function. The test statistics are continuous functionals of a sequential marked empirical process which combines classical CUSUM tests with marked empirical process approaches well known from goodness of-fit testing. Weak convergence to a Gaussian process is shown under the null hypothesis in the case of a strictly stationary strongly mixing process. We obtain very simple limiting distributions and distribution-free tests in the case of univariate covariates. In contrast to simple CUSUM type tests the new tests are consistent against general change point alternatives. To obtain tests that react sensitive only to changes in the regression function in cases where also changes in the conditional variance function may appear, we suggest bootstrap versions of the tests.