The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is also given.