Using first-principles total-energy calculations, we have studied the adsorption of In on the Ge(001)-(2x2) and partially H-passivated Ge(001)-(2x4) surface. We have used two possible orientations for the In ad-dimers adsorption on this surface: (i) the In ad-dimers parallel to the underlying Ge dimers (Model I) and (ii) the In ad-dimers orthogonal to the underlying Ge dimer (Model II). For the Ge(001)-(2x2) surface, we have found that the In ad-dimers parallel model (Model I) is energetically favourable by 0.46 eV/ad-dimer compared to the In ad-dimers orthogonal model (Model II). It is comparable with the value of 0.37 eV/ad-dimer, calculated by Takeuchi using first-principles total-energy calculations. For the partially H-passivated Ge(001)-(2x4) surface, we have found that Model I is energetically favourable by 1.97 eV/ad-dimer compared to Model II. We have also presented a discussion of the electronic states for the energetically favourable structures. (C) 2004 Published by Elsevier B.V.