This paper is concerned with robust estimation of change points in regrt!ssion models, possibly with trending regressors. We obtain the rate of convergence and the asymptotic distribution of M-estimators of the regression coefficients and the change point with serially dependent observations. The asymptotic properties of the estimators are developed assuming that the size of the jump is fixed as well as it shrinks to zero as the sample size increases. In the first case, the asymptotic distribution of the change point estimator is difficult to tabulate. The performance of asymptotic inferences in practice is illustrated by means of Monte Carlo simulations
