Spectroscopic ellipsometry studies in the energy range from 0.7 up to 5.5 eV were carried out in order to determine the dielectric function (DF) of ‘narrow’ band gap (< 1 eV) single-crystalline InN films grown by molecular beam epitaxy on sapphire substrates. The imaginary part of the DF is characterized by a strong increase immediately above the band gap and then by a nearly constant value up to 4 eV. Pronounced structures above 4 eV are attributed to transitions along the L-M direction in the Brillouin-zone as a comparison with first-principles calculations indicates. In contrast, sputtered layers (band gap ∼1.9 eV) studied for comparison show a completely different spectral shape of the DF. Finally, DF's of high In-content InGaN alloys are presented, providing further evidence that InN is a “narrow” band gap semiconductor.