The results of studies of the spontaneous photoluminescence and stimulated emission spectra of epitaxial n-InN layers with a concentration of free electrons of ~10¹⁹ cm^–3 are reported. The layers are grown by molecular-beam epitaxy with the plasma activation of nitrogen on sapphire substrates with AlN and GaN buffer layers. It is found that, as the InN layers are grown under conditions with enrichment with nitrogen at a growth temperature elevated to 470°C close to the beginning of the decomposition of InN, the crystal quality of the layers is improved and the stimulated-emission threshold is lowered. As the conditions of growth change to conditions with enrichment with the metal, two emission bands separated by an energy of 100 meV are observed in the spontaneous-photoluminescence spectra of InN. For such layers, a substantial increase in the stimulated-emission threshold and, in some cases, the lack of a transition to stimulated emission are observed. In the study, an interpretation of the observed emission bands is given and some inferences as to their nature are made.