The adsorption structures of self-assembled monolayers (SAMs) formed at saturation coverages of 1-octanethiol SAMs, prepared under ultrahigh vacuum UHV conditions on Cu(111) and Ag(111) substrates, were measured using a normal-incidence X-ray standing wave (NIXSW) technique. A thorough and pedagogical exposition of the relationship between the structural parameters determined in NIXSW and a number of simple adsorption structures is presented. In the two SAMs studied, the NIXSW data indicated the formation of monolayers which induced a reconstruction of the outermost layer of the substrate. SAMs on Cu and Ag were indistinguishable using the NIXSW technique, but given the different steric requirements imposed by each surface it is proposed that a different adsorption geometry is adopted in each case, which is either incommensurate with the underlying substrate or commensurate on a large mesh. In the case of Ag(111) the NIXSW data are consistent with the formation of a distorted (root 7x root 7)R19.1 degrees structure, proposed by other workers. In the case of Cu(111), it is proposed that the adsorbate structure is most likely a significant distortion of the (root 3 x root 3)R30 degrees structure observed in SAMs of alkanethiols on Au(111) and we speculate on the existence of an overlayer of CH3-(CH2)(7)-S-Cu-3 clusters.