We propose an estimation procedure for (semiparametric) panel data censored regression models in which the error terms may be subject to general forms of non-stationarity, thus permitting heteroscedasticity over time. The proposed estimator exploits a weak structural form imposed on the individual speciic eeect. This is in contrast to the estimators introduced in Honor e(1992) where the individual eeect was left completely unspeciied, but a stationarity assumption was imposed on the error terms. We adopt a two-stage procedure based on nonparametric quantile regression, similar to that used in Khan(1997a,b) and Chen and Khan(1998). An attractive feature about this approach is that it allows for very general forms of cross sectional conditional heteroscedasticity as well. Furthermore, the proposed procedure can be easily extended to estimate a more general class of censored panel data models which allow for time varying loading factors on the individual speciic eeects. The proposed estimators are shown to be p n-consistent and asymptotically normal under regularity conditions which are common in the literature. A small scale simulation study is conducted to illustrate both the nite sample properties of these estimators as well as the sensitivity of Honor e's estimator to non-stationary errors.