The nonlinear interaction, due to quantum electrodynamical effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner–Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics are determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to the break-up and focusing of ultra-high-intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser–plasma systems.