Nickel and rhodium (001) surfaces display a similar (in terms of scanning tunneling microscopy images) clock reconstruction when half a monolayer of C–Ni, N–Ni or O–Rh is adsorbed; no reconstruction is observed instead for O–Ni. Adsorbate atoms sit at the center of the black squares of a chess-board, c(2×2), pattern and two different reconstructions are actually compatible with the observed STM images — showing a (2×2)p4g pattern — according to whether a rotation of the black or white squares occurs. We report on a first-principles study of the structure of X–Ni(001) and X–Rh(001) surfaces (X=C, N, O) at half a monolayer coverage, performed using density-functional theory. Our findings are in agreement with all available experimental information and shed new light on the mechanisms responsible for the reconstructions. We show that the same substrate may display different reconstructions (or no reconstruction) upon adsorption of different atomic species, depending on the relative importance of the chemical and steric factors that determine the reconstruction. © 1999 Published by Elsevier Science B.V. All rights reserved.