The bonding in Ks(8)In(11) and Rb8In11 has been investigated at the SCF level with the periodic Hartree-Fock method. Comparison is made with In-11 clusters with formal charges 7- and 8- calculated at the same level. The structure of the 7- cluster has been optimized; it significantly differs from the structure observed in the condensed phase. The second anion (8-) is found to be dissociative. Moreover, the indium Mulliken populations in dusters are dramatically different from those calculated for the solid phase. This indicates that the reliability of the cluster approach is highly questionable. The stability of the solid phases is mostly due to the electrostatic interactions between the anionic clusters and the alkali counterions. The integrated charge density in the cation region is consistent with a picture in which an electron is delocalized over the potassium layers. The band structure and density of states of the solid phases are discussed. Both K8In11 and Rb8In11 are found to be weak electronic conductors. At the present state of the art, it is not possible to assess the charge borne by the indium cluster and, therefore, to decide whether one or more electrons are delocalized over potassium layers. The bonding in these systems has been investigated from the topological analysis of the electron localization function point of view. The bonding in the In-11 anionic clusters is characterized by a network of attractors lying 1 Angstrom outward from the indium centers.