A brief introduction into the large importance of relaxation processes in the electron gas for the understanding of various transient processes in low temperature plasmas is given. Based on comprehensive, strictly non-hydrodynamic studies on the electron relaxation by using kinetic approaches the large variety of the temporal and spatial electron relaxation in atomic and molecular plasmas is elaborated and demonstrated under different plasma conditions. The analysis has been performed particularly with respect to the relaxation behavior of the electron energy distribution function and the associated energy and momentum dissipation in electron collisions as well as the resultant characteristic overall relaxation times and relaxation lengths. Especially the temporal and spatial relaxation, respectively, is considered under field-free conditions in decaying plasmas, under the action of constant electric fields leading to the formation of steady states and under the action of temporally or spatially periodic fields. Moreover, the complex spatiotemporal transient behavior of the electron gas into a spatially structured, time-independent state is considered. To simplify the representation, all results on the temporal and spatial relaxation have been deduced using corresponding two-term approximations, but could be performed as well with available multi-term approaches without effecting significant changes in the deduced basic relaxation characteristics. (C) 2002 Elsevier Science B.V. All rights reserved.