It is believed that lateral interactions play an important role in chemisorption site selection. With the advent of angular resolved and polarization dependent photoemission spectroscopies, one is able to compare computed band structure with angular resolved photoemission data. This advance coupled with theoretical calculations provides an excellent opportunity for investigating direct (adsorbate-adsorbate) and indirect (through-substrate) lateral interactions at surfaces. We have modelled the chemisorption of oxygen on Al(111) using direct lateral interactions only (isolated monolayer). The calculated results provide a good framework for interpreting the data. For O2 monolayer the direct lateral interactions are also appreciable and lead to significant dispersion in the calculated energy bands. We have also computed the electronic structure for two dimensional isolated layers of CO in ordered configurations observed on a Pd(100) surface. The shape and width of the 4σ-derived band is satisfactorily accounted for by this direct lateral interaction only model. Having demonstrated that direct lateral interactions lead to observable band dispersions, it is suggested that they might influence normal vibrational frequencies and ought to be included. © 1983.