Two-dimensional hafnium diselenide (HfSe2) and hafnium disulfide (HfS2) have impressive theoretical properties but are among the less well-studied transition metal dichalcogenides. Further research is needed to realize high-performance Hf-based devices. We investigated the air stability of mechanically exfoliated layers of HfSe2 and HfS2 via atomic force microscopy and Raman spectroscopy studies. With continued exposure to air, the surface of HfSe2 progressively transforms from HfSe2 to HfOx and Se, as confirmed by changes in Raman spectra and by the appearance of Se-rich, spire-like features. We determined that sample thickness, total time of air exposure and and exfoliation in a glove box versus in air all affect the degree of transformation. HfS2 was much more stable in air and served as a comparison for the study of HfSe2. This work lays out initial steps toward controlling the behavior of HfSe2 surfaces, which can inform future efforts to fabricate Hf-based transistors.