We present an extensive density functional theory (DFT) study of adsorption site energetics for oxygen and sulfur adsorbed on two vicinal surfaces of Cu and Ag, with the goal of identifying the most stable adsorption site(s), identifying trends and common themes, and comparing with experimental work in the literature where possible. We also present benchmark calculations for adsorption on the flat (111) and (100) surfaces. The first vicinal surface is the (211), and results are similar for both metals. We find that the step-doubling reconstruction is favored with both adsorbates and is driven by the creation of a special stable fourfold hollow (4fh) site at the reconstructed step. Zig-zag chain structures consisting of X–M–X units (X = chalcogen, M = metal) at the step edge are considered, in which the special 4fh site is partially occupied. The zig-zag configuration is energetically competitive for oxygen but not sulfur. DFT results for oxygen agree with experiment in terms of the stability of the reconstruction, but contradict the original site assignment. The second vicinal surface is the (410), where again results are similar for both metals. For oxygen, DFT predicts that step sites are filled preferentially even at lowest coverage, followed by terrace sites, consistent with the experiment. For sulfur, in contrast, DFT predicts that terrace sites fill first. Oxygen forms O–M–O rows on the top edge of the step, where it occupies incomplete 4fh sites. This resolves an experimental ambiguity in the site assignment. For both the (211) and (410) surfaces, the interaction energy that stabilizes the X–M–X chain or row correlates with the linearity of the X–M–X unit, which may explain key differences between oxygen and sulfur.