Abstract. First principles calculations of clean and adsorbate-covered surfaces of Si(001) and Ge(001) are reported. Chemical trends in the adsorption of ordered Na, K, Ge, As, Sb, S, Se and CI overlayers are discussed. The calculations are based on the local-density approximation and employ non-local, norm-conserving pseudopotentials together with Gaussian orbital basis sets. The semi-infinite geometry of the substrate is properly taken into account by employing our scattering theoretical method. From total-energy minimization calculations we obtain optimal surface reconstructions which show asymmetric dimers for Si(001), Ge(001) and Ge:Si(001). For As:Si(001), Sb:Si(001) and Sb:Ge(001), we find symmetric adatom dimers in the equilibrium geometries. S or Se adlayers are found to be adsorbed in bridge positions forming a (1 x 1) unit cell with a geometry very close to the configuration of a terminated bulk lattice. C1 atoms adsorb on top of the dangling bonds of symmetric Si dimers residing in the first substrate-surface layer. Our calculations for Na:Si(001) and K:Si(001) confirm valleybridge site adsorption for half monolayer coverage. For full monolayer alkali-metal coverage, adsorption in pedestal and valley-bridge positions is found to be energetically most favourable. The calculated optimal adsorption configurations are in excellent agreement with a whole body of recent experimental data on surface-structure determination. For these structural models, we obtain electronic surface band structures which agree very good with a wealth of data from angle-resolved photoemission spectroscopy investigations. The adsorption of adlayers at semiconductor surfaces has been under intensive study in recent years. These investigations are motivated by fundamental physical reasons and important technological applications. In basic research, semiconductors are interesting substrates for adsorption systems due to the unsaturated directional bonds at their surfaces. This allows the formation of chemical compounds which are neither stable as small, isolated molecules nor as extended solids. The technological interest ranges from homoand heteroepitaxy and growth, via surface passivation and doping to dry etching and photo-surface cleaning. For example, the quality of the heteroepitaxial growth of GaAs on Si is determined by the initial stage of this process which consists in formation of As adlayers. Furthermore, surface passivation may involve As, S or Se atoms. In the fabrication of electronic devices, dry etching and photo-surface cleaning is carried out by the reaction of C1 on Si. The adsorption of alkali metals in the range of monolayer coverage leads to a drastic reduction of the ionization energy. These systems have important applications as high-efficiency emitters. They are also widely discussed in the context of the Schottky-barrier problem [1].