In the frame of extended kinetic theory, a kinetic model is proposed, which allows for elastic and inelastic scattering. The gas atoms have an internal structure, namely an arbitrary finite number of internal energy levels. Transitions between different energy levels may occur by absorption or emission of photons of the self-consistent radiation field as well. The main properties of the global collision operator are investigated, equilibria are determined, and an H theorem is proved. The transport problem of a swarm of single level test particles diffusing in a background of multilevel field particles is then discussed along the same lines.