Tests based on the quantile regression process can be formulated like the classical Kolmogorov–Smirnov and Cramér–von–Mises tests of goodness–of–fit employing the theory of Bessel processes as in Kiefer (1959). However, it is frequently desirable to formulate hypotheses involving unknown nuisance parameters, thereby jeopardizing the distribution free character of these tests. We characterize this situation as “the Durbin problem” since it was posed in Durbin (1973), for parametric empirical processes.