We extend the theory of photonic crystals to account for the influence of non-linear materials and, in particular, for the dependence of the photonic density of modes on the intensity level of transiting electromagnetic fields. The non-linear band structure problem is solved as a convergingsequence of ordinary, linear, band structure calculations. These computations suggest that the adaptation of the gap location and width to the occupation of one of the photon modes could be used for light-controlled adjustment of transmission spectra.