The atomic geometry, c hemical bonding and energetics for full -, 2 3, 1 2 and 1 3 of a monolayer of Te c o verages on the Si 001 Te -1 1 , 2 1 , and 3 1 surfaces have been studied employing rst -principles total-energy calculations. For one monolayer coverage we nd that the 1 1 structure is energetically favourable against 2 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 1 -reconstruction, is an energetically stable con guration. At 1 3 coverage, we h a ve obtained the formation of Si-Si dimers with a single Te atom, at the surface in a 3 1 -reconstruction. In this structure there is a very weak interaction between the dimer and the single Te atom.