We study a CUSUM-type test for detecting changes in regression quantiles under strong mixing. For independent time series this test already was studied by Qu (2008). Applying this test to dependent data poses some additional challenges. For testing in a single regression quantile we propose a Carlstein (1986) type subsampling based estimator to standardize the statistic. For testing across multiple regression quantiles we use a bootstrap based method proposed by Inoue (2001) to compute critical values. The performance of the method is evaluated via simulation studies.