Following Gehan (1965)and Breslow(1970), a generalization of Steel's(1959)test for comparing several treatments with acontrol in a one-way layout when observations are subject to the same pattern of random right-censorship is proposed. The proposed test is constructed mainly for testing against simple-tree alternatives. However, based on the test, a multiple testing procedure for deciding which treatments(if any)are better than the control is suggested. The relative level and powerperformances of the proposed testing procedure and the ones suggested respectively by Magel(1988)and Chakraborti(1990) areexamined in a Monts\e Carlo study