Tests which are specific for location are developed in the k-sample situation with right-censored data. The tests are based on general estimating functions, and do not require full parametric assumptions for large samples, but in general they are not based only on ranks. One class of tests allows shapes to differ in the k populations, and includes as a special case the median test of \textit{R. Brookmeyer} and \textit{J. Crowley} [J. Am. Stat. Assoc. 77, 433-440 (1982; Zbl 0495.62054)]. If the distributions are assumed to differ at most in location, modified tests are suggested in which survival function estimates are obtained by pooling the data from all samples. \textit{R. L. Prentice}'s [Biometrika 65, 167-179 (1978; Zbl 0377.62024)] median test, with minor modifications, is included in this class.