The electronic structure of the recently reported (Ca(7)N(4))[M((x))] (M = Ag, Ga, and In) phases has been studied by means of first principles density functional theory (DFT) calculations. It is shown that under the assumption of very weak host-guest interactions: (a) four calcium atoms per formula unit may be considered as Ca(1.5+), whereas the remaining three may be considered as Ca(2+) so that the guest atoms would be neutral, and (b) the Peierls distortions which could set in the guest linear chains are unlikely. These results are compatible with the experimental information. However, the first principles DFT calculations clearly show that very sizable host-guest interactions occur and drastically modify this situation. As a result, there is a substantial electron transfer from the framework to the guest atoms, and all calcium atoms of the framework are better described as Ca(2+). The stoichiometry and structure of these systems result from a competition between the natural tendency of the bare guest atoms to form uniform linear chains within the reduced space of the channels and the attempt to optimize their positions within the channels through interactions with the calcium atoms. Model calculations suggest that indium has a weaker tendency to form uniform linear chains and interacts in a stronger way with the host. It is shown that, for the (Ca(7)N(4))[M(1.33)] (M = Ag and Ga) phases, a structure built from three repeat units of the Ca(7)N(4) host framework containing uniform linear chains with a repeat unit of four guest metal atoms is compatible with the strong interaction scenario and the lack of correlation between the different linear guest chains. These phases should be metallic conductors, and the carriers have both host and guest character. In contrast, the guest atoms in (Ca(7)N(4))[In(1.0)] prefer to occur as a series of trimeric units. Although this phase is found to have a metallic band structure, the conductivity should be smaller than those of the (Ca(7)N(4))[M(1.33)] (M = Ag and Ga) phases.