We deal with nonparametric estimation in a nonlinear cointegration model whose regressor and error term can be contemporaneously correlated. The asymptotic properties of the Nadaraya-Watson estimator are already examined in the literature. In this paper, we consider nonparametric least absolute deviation (LAD) regression and derive the asymptotic distributions of the local constant and local linear estimators by appealing to the local time approach. We also present the results of a small simulation study.