The surface ″phases″ observed by LEED and other techniques in adsorption studies are usually ascribed to pairwise interactions between the adsorbate and the substrate, and between the adsorbed species themselves. However, in the case of chemisorbed hydrogen - and probably other overlayers - on W(100) and Mo(100) the phase changes appear to involve an adsorbate-induced reconstruction of the substrate. The structures are similar to those observed on the clean substrates at low temperture and they are characterized by a periodic lattice distortion whose wave vector depends on the adsorbate density and the temperature. Presumably the driving mechanism involves a lowering of the surface electronic energy and the periodicity may therefore reflect the geometry of the two-dimensional Fermi surface.