We study the deep levels in InAlN nearly lattice-matched to GaN by photocapacitance spectroscopy. This technique allows the study of very deep levels having too slow thermal emission rates to be detected by other deep level spectroscopy techniques. We will identify a broad band of deep levels centered 1.7 eV below the InAlN conduction band edge. The deep level band is characterized by a negligible Franck-Condon shift and by a broadening parameter Delta E = 0.38 eV. Furthermore, we will show evidences for a second class of deep levels with optical ionization energy >2 eV, which will be attributed to previously reported oxygen-related DX centers. Published by AIP Publishing.