This paper presents orthogonality conditions for censored regression models with fixed effects and lagged dependent variables. The orthogonality conditions can be used to construct method of moments estimators of the parameters of the model. Nonlinear fixed effects models are usually estimated by maximum likelihood, with fixed effects treated as parameters to be estimated. Monte Carlo results indicate that in a Tobit model with fixed effects and lagged dependent variables, the maximum likelihood estimator of the effect of the lagged dependent variable performs poorly. The method of moments estimator based on the orthogonality conditions presented here, however, performs quite well.