Although the theory of asymptotically most powerful rank tests is fairly well developed, only little attention (see [4]) has been paid to censored data. In this paper we derive the a.m.p.r.t. for censored data from the a.m.p.r.t. based on the complete sample. For simplicity, we consider the two-sample location problem for data censored on the right. The methods used, however, can be applied to find the a.m.p.r.t. for multi-censored data and also the a.m.p.r.t. for the two-sample dispersion problem when the data are censored.