The infrared region of bosonic systems typically involves large fields and strong nonlinearities and may even lead to Bose condensation in far-from-equilibrium situations. The latter is observed in scalar theories close to a non thermal fixed point, where the distribution function follows a self-similar evolution with universal scaling properties. While an ordinary kinetic theory fails to describe the observed, we show that the large-N kinetic theory, an effective kinetic theory derived within a 1/N expansion to NLO, is able to give a quantitative description of the observed lattice simulation results. It is thus possible to provide a kinetic description of a bosonic theory that only contains quasiparticle degrees of freedom at all momentum modes, even in the deep infrared.