The Kolmogorov-Smirnov test is important in nonparametric statistical inference. The limiting distribution of the Kolmogorov-Smirnov statistic under the null hypothesis is well known and has been derived by several different methods. The limiting distribution of this statistic under the alternative hypothesis is unknown so that it is not possible, in general, to compute the power of the Kolmogorov-Smirnov test.