In this paper the kinetics of excitation, quenching, and absorption in an e-beam pumped KrF laser is discussed. It is argued that under usual experimental conditions the steady-state approximation can be applied. For that case a comprehensive kinetic model can be treated analytically. The model simulates quite well the experimental results obtained so far. It predicts the maximum performance conditions, limiting behaviour, and scaling properties of e-beam pumped KrF lasers.