SUMMARY A class of two-sample nonparametric tests for location and scale shift, simultaneously, is proposed. The asymptotic distribution of the proposed class is obtained both under the hypothesis and alternative. Using this result it is shown how the asymptotic relative efficiency of tests in the proposed class can be obtained. F2(x) = F(a2x +4f2), respectively. The purpose of this paper is to study a class of two-sample nonparametric test statistics which can be used to test HO: Fl(x) = F2(x) = F(x) for all real x, versus the alternative Ha:acc * a2 or /h t /h' or both. The proposed statistics will be expressed as functions of two nonparametric statistics, one sensitive to scale shift and the other to location shift. Lepage (1971) proposed a statistic which is a combination of the Wilcoxon and Ansari- Bradley statistics. Furthermore, he showed that since the Wilcoxon and Ansari-Bradley statistics are uncorrelated under Ho, his proposed statistic has a limiting central chi- squared distribution with two degrees of freedom. Thus the critical values needed to carry out an approximate test of Ho can be obtained from a standard chi-squared table. The question regarding the asymptotic power behaviour of Lepage's statistic is of interest but is not, however, discussed by Lepage. Thus the asymptotic relative efficiency of the proposed statistics will also be discussed, as a means of comparing such statistics.