The crystal structure of the ternary solid solutions GaxAl1-xN, InxGa1-xN and InxAl1-xN is described theoretically on the microscopic level, and the energies of internal strain in these solutions are calculated in terms of the valence-force-field model. For the solid solutions InxGa1-xN and InxAl1-xN the internal strain energy is an important parameter inasmuch as it is responsible for the existence of a broad miscibility gap in which solid solution formation is possible under thermodynamically nonequilibrium conditions. At the same time the miscibility gap does not present any serious problem for the GaxAl1-xN solid solutions. In view of the tendency for spinodal decomposition, common for these materials, the InxGa1-xN and InxAl1-xN solid solutions can also be synthesized over a wide range of compositions under thermodynamically nonequilibrium conditions that ensure formation of metastable single-phase solid solutions. Formation of InxGa1-xN and InxAl1-xN solid solutions with x = 0.25, 0.50 and 0.75 as superstructures immediately in the course of their synthesis is the most likely event.