The homogeneity and stability of TEA‐Excimer laser discharges strongly depend on the preionization. A homogeneous discharge can only develope if it is ensured that the electron density exceeds a certain level at the moment of the ignition. The kinetic of these electrons during the preionization is analyzed theoretically by the use of the Boltzmann equation for x‐ray preionized KrF* laser systems. The time dependent velocity distribution of the electrons is calculated for different buffer gases and gas mixtures. The resulting electron densities and life times are discussed and compared with experimental investigations. It is quantitatively shown at the first time that the kind of the buffer gas has a decisive influence on the velocity distribution, density and life time of the preionization electrons.