A method is proposed for testing normality, in the case of general Type II censored data—that is, data for which only a subset of the order statistics are available. Three test statistics are proposed, which are generalizations of the statistics proposed in LaRiccia (1986), and have many of the same properties. Specifically, they are designed to be asymptotically optimal with respect to specific alternatives and are easily adjusted to be asymptotically optimal with respect to many other types of alternatives. Under the null hypothesis, irrespective of the type or amount of censoring, the proposed test statistics are asymptotically distributed as chi-squared random variables. Further, results of a simulation study are presented, indicating that these statistics converge quite rapidly in distribution to the appropriate chi-squared random variables and that the asymptotic critical values provide a useful approximation to the small sample critical values even forn= 25. The results of a simulation study comparing the power of the proposed tests with some standard tests of normality are presented. These results indicate that, for the cases considered, these statistics compare favorably with the standard procedures.