It has been suggested that the appearance of nonvariable stars within the Cepheid strip could be explained by a range in the helium abundance of Population I stars. In order to study this possibility, spectra were obtained of the main-sequence B stars in the galactic cluster NGC 129, which contains a nonvariable Cepheid-strip star, and M25, which contains a relatively hot Cepheid. Unfortunately, several of the stars in these clusters turn out to be helium-weak stars. In NGC 129 two stars which appear normal give a normal abundance, while in M25 all of the observed stars have abnormally low abundances. The significance of the low abundance in M25 is not clear. The abundance in NGC 129 is not low enough to support the above suggestion. 4 figures, 2 tables.