Abstract. A kinetic model for a gas mixture consisting of three species of structureless particles and one species of two-level atoms is considered. Elastic scattering and chemical reactions are taken into account, along with (de-) excitation processes triggered by inelastic collisions and interactions with photons. Two different strategies are proposed in order to obtain approximate solutions from the kinetic model. The former resorts to the derivation of a closed set of macroscopic equations in a proper asymptotic limit (moment-equation approach); the latter applies a suitable discretization of the extended kinetic equations (semi--continuous approach). Numerical solutions to spatially homogeneous test cases are provided and compared.