The atomic geometry, chemical bonding and energetics for full -, 2/3, 1/2 and 1/3 of a monolayer of Te coverages on the Si(001)/Te -(1 x 1), (2 x 1), and (3 x 1) surfaces have been studied employing first - principles total-energy calculations. For one monolayer coverage we nd that the (1 x 1) structure is energetically favourable against (2 x 1) structure, in agreement with experimental results, indicating that the dimerization of Te atoms is not an exothermic process. For a coverage of 2/3 of a monolayer, the formation of Te-Si-Te mixed trimers, in a (3 x 1) - reconstruction, is an energetically stable configuration. At 1/3 coverage, we have obtained the formation of Si-Si dimers with a single Te atom, at the surface in a (3 x 1) - reconstruction. In this structure there is a very weak interaction between the dimer and the single Te atom.