. We consider a general non-parametric regression model, where the distribution of the error, given the covariate, is modelled by a conditional distribution function. For the estimation, a kernel approach as well as the (kernel based) empirical likelihood method are discussed. The latter method allows for incorporation of additional information on the error distribution into the estimation. We show weak convergence of the corresponding empirical processes to Gaussian processes and compare both approaches in asymptotic theory and by means of a simulation study.