Horváth et al. [8] developed a monitoring procedure for detecting a change in the parameters of a linear regression model having independent and identically distributed errors. We extend these results to allow for dependent errors, which need not be independent of the stochastic regressors, and we also provide a class of consistent variance estimators. Our results cover strongly mixing errors as an important example. Applications to autoregressive time series and near-epoch dependent regressors are discussed, too.