  This paper discusses asymptotically distribution free tests for the classical
goodness-of-fit hypothesis of an error distribution in nonparametric regression
models. These tests are based on the same martingale transform of the residual
empirical process as used in the one sample location model. This transformation
eliminates extra randomization due to covariates but not due the errors, which
is intrinsically present in the estimators of the regression function. Thus,
tests based on the transformed process have, generally, better power. The
results of this paper are applicable as soon as asymptotic uniform linearity of
nonparametric residual empirical process is available. In particular they are
applicable under the conditions stipulated in recent papers of Akritas and Van
Keilegom and M\"uller, Schick and Wefelmeyer.
