A powerful and a stable numerical method is developed to solve the Boltzmann equation of electrons moving under the action of an electric field in weakly ionized gases involving space and time gradients. It is based on the classical two term development of the distribution function and on a strongly implicit procedure following position and energy axis and an explicit approach along the time axis. This numerical algorithm is successfully applied to determine the spatiotemporal variation of the electron distribution function and the associated swarm parameters (mean energy, drift velocity, ionization and attachment coefficients, etc.) in the case of nonthermal electrical discharges in different gases (He, Ar andO2)under different applied electric fields and initial and boundary conditions. The transient phase, the following steady state phase and also the electrode effects are clearly emphasized and analyzed for each gas discharge studied. ©1997 American Institute of Physics.