The impact of duration response measurement error is investigated by using small variance approximations. The inconsistency of GMM estimators that ignore measurement error is studied for both single spell models with right censoring, and for a two spell lagged duration dependence model. The results suggest a corrected GMM estimator for the error free and measurement error distributions. When the error free density is known, identification is achieved by using the moment condition that defines the measurement error sensitive specification score test. The results are applied to unemployment duration data from the BHPS.