A description is given of a detailed nonsteady-state multiwave kinetic model of a laser, based on xenon atom transitions with λ = 1.73, 7.03, 2.65, 2.63, 3.37, and 3.51 μm in an He — Ar — Xe mixture pumped by a hard ioniser. The proposed kinetic model is tested against the results of experiments on electron-beam pumping of an Xe laser containing pure xenon, as well as binary and ternary mixtures. Numerical modelling is used to identify the main mechanisms pumping the upper active levels: three-particle recombination of atomic Xe+ ions (He — Xe mixture), dissociative recombination of molecular Xe2+ ions (pure Xe), dissociative recombination of molecular ArXe+ ions and electron excitation from the 6s' xenon atom states in an (He) — Ar — Xe mixture. It is shown that the contribution of each of the mechanisms to pumping of the upper active level is determined by the composition and pressure of the mixture.