Molybdenum K-edge EXAFS studies have allowed us to determine the local order in the layered materials Li2-MoO3, Li4Mo3O8, LiMoO2, and H2MoO3. The presence of Mo3 metal-metal-bonded triangles in Li2MoO3, with d(Mo-Mo) = 2.580(1) angstrom (x 2), is unequivocally demonstrated for the first time. This information cannot be obtained from diffraction experiments because the system is intrinsically disordered. Triangular clusters are also found in the related Mo(IV)-containing lithium molybdate Li4Mo3O8 and in H2MoO3, prepared from Li2MoO3 by ion exchange (d(Mo-Mo) = 2.560(1) angstrom (x 2) and 2.506(1) angstrom (x 2), respectively). The metal-metal bonding in the Mo(III)-containing oxide LiMoO2 is shown to be more complex than diffraction studies had indicated. In LiMoO2, Mo-Mo-bonded chains are formed, and we present a possible model containing disordered chains, with d(Mo-Mo) = 2.561(2) angstrom (x 2) and 2.709(2) angstrom (x 2), found in the MoO2 sheets.