The X test proposed by VAN DER WAERDEN is a nonpararnetric procedure for testing whether two independently drawn samples result from the same population VAN DER WAERDEN and NIEVERGELT have also given a table of critical values of this X test, but it is too smail for some practical purposes. I n the present pape.the table has been enlarged and checked thereat. Here the critical values are calculated by a new asymptotic formula. developed in the paper. Generally the accuracy of the so obtained approximative values is better than the former used ones.