The authors have studied the electronic structure of InN and GaN employing G0W0 calculations based on exact-exchange density-functional theory. For InN their approach predicts a gap of 0.7 eV. Taking the Burnstein-Moss effect into account, the increase of the apparent quasiparticle gap with increasing electron concentration is in good agreement with the observed blueshift of the experimental optical absorption edge. Moreover, the concentration dependence of the effective mass, which results from the nonparabolicity of the conduction band, agrees well with recent experimental findings. Based on the quasiparticle band structure the parameter set for a 4×4 k∙p Hamiltonian has been derived.