%0 Journal Article %T On the BRST Operator of $W$-Strings %A E. Bergshoeff %A H. J. Boonstra %A M. de Roo %A S. Panda %A A. Sevrin %J Physics %D 1993 %I arXiv %R 10.1016/0370-2693(93)90598-C %X We discuss the conditions under which the BRST operator of a $W$-string can be written as the sum of two operators that are separately nilpotent and anticommute with each other. We illustrate our results with the example of the non-critical $W_3$-string. Furthermore, we apply our results to make a conjecture about a relationship between the spectrum of a non-critical $W_n$-string and a $W_{n-1}$-string. %U http://arxiv.org/abs/hep-th/9303051v2