The structures of the clean “(1 × 1)” and the “c(2 × 2)” sulfur-covered molybdenum (100) surfaces have been studied by low-energy electron diffraction (LEED) intensity analyses. It is found that the atoms in the top layer of both these surfaces probably reside at asymmetrical adsorption sites, destroying the perfect (1 × 1) and c(2 × 2) periodicities normally deduced from the LEED patterns. For clean room-temperature Mo(100), a slight preference is found for the topmost atoms to be displaced 0.13 ± 0.05 Å away from the centers of hollow sites of the second metal layer. This displacement occurs in the four equivalent 〈11〉 surface directions (diagonally in the square surface lattice), possibly randomly. The clean surface exhibits first, second and third interlayer spacing relaxations of − 6% ± 1.5%, 2% ± 2% and 0.5% ± 3%, respectively, relative to the bulk interlayer spacing. In the “c(2 × 2)” sulfur overlayer, the sulfur atoms are found to reside away from the center of hollow sites by 0.20 ± 0.05 Å. This displacement occurs in the four equivalent 〈10〉 surface directions (parallel to the sides of the square metal lattice cells), possibly randomly. The sulfur-Mo interlayer spacing is 1.03 ± 0.02 Å, while the spacings between metal layers have relaxed closer to their bulk value, which a top metal-metal spacing still contracted by 3% ± 3%. The asymmetrical site gives rise to three different bond lengths between sulfur and molybdenum atoms: 2.33 and 2.58 Å for Mo atoms in the topmost metal layer, and 2.56 Å for Mo atoms in the second metal layer. In this case, no lateral Mo relaxations were investigated.