  U-quantiles are applied in robust statistics, like the Hodges-Lehmann
estimator of location for example. They have been analyzed in the case of
independent random variables with the help of a generalized Bahadur
representation. Our main aim is to extend these results to U-quantiles of
strongly mixing random variables and functionals of absolutely regular
sequences. We obtain the central limit theorem and the law of the iterated
logarithm for U-quantiles as straightforward corollaries. Furthermore, we
improve the existing result for sample quantiles of mixing data.
