The impact of different collision processes of the electrons with the gas atoms on their spatial relaxation under the action of space-independent electric fields is analyzed in a weakly ionized, collision-dominated helium plasma. Based on the numerical solution of the one-dimensional inhomogeneous electron Boltzmann equation, the spatial evolution of the electron velocity distribution function and of the related macroscopic quantities is investigated for different models concerning the treatment of the elastic, exciting, and ionizing collision processes. The spatial relaxation into homogeneous states is initiated by a disturbance which is directly imposed on the electron velocity distribution as a boundary condition. At moderate and higher electric fields this disturbance excites spatially periodic structures in the distribution function which ale damped out by special mechanisms inherent in the exciting and ionizing collision processes. With decreasing field strength the damping due to the energy loss in elastic collisions becomes more effective and causes at lower fields an aperiodic establishment into homogeneous states.