To investigate the adsorption properties of the Cadmium and Mercury Telluride surfaces, a model for adsorption on narrow gap semiconductors is set up. The adsorption of a Cs atom at an ‘atop’ site (over a single surface atom) and a Zn atom at a centered site (in the centre of three surface atoms) on Tellurium terminated surfaces are studied. Results are presented for the bulk band structures, the localised surface states, the density of states of the Tellurium (111) surfaces. The adsorption properties calculated are (i) the change in density of states, (ii) charge densities and (iii) binding energies s functions of the adsorption parameters. We observe a change in the adatom density of states as the coupling strength to the surface is increased from a broadened atomic level to a complex structure. We also see a maximum in the occupation number and a minimum in the binding energy as the Fermi level is swept through the adatom affinity level.