The spatiotemporal relaxation of electrons in spatiallyone-dimensional plasmas acted upon by electric fields isinvestigated on the basis of the space- and time-dependentelectron Boltzmann equation. The relaxation process is treatedusing the two-term approximation of an expansion of the electronvelocity distribution function in Legendre polynomials. To verifythe complex Boltzmann equation approach by a completelyindependent kinetic method, results for inhomogeneous column-anodeplasmas of glow discharges between plane electrodes are comparedwith corresponding ones obtained by Monte Carlo simulations. Thespatiotemporal electron relaxation in argon plasmas, subjected toa space-independent electric field and maintained by atime-independent inflow of electrons at the cathode side of theplasma region, is considered. Starting from steady state at agiven electric field, the relaxation process is initiated by apulse-like change of the electric field strength and is traceduntil the spatially structured, time-independent state associatedto the changed field is reached. The behaviour of the velocitydistribution function and macroscopic quantities of the electronsin space and time is analyzed for enlarged and reduced electricfield strengths typical of the column region of glow discharges.In particular, the spatiotemporal reformation of plasma structureshas been found to progress in two phases, i.e., existingstructures in the distribution are driven to merge in wide plasmaregion first, followed by a formation phase of new spatialstructures which are induced by the cathode-sided inflow ofelectrons. The results for the macroscopic quantities and theisotropic distribution functions obtained by Boltzmann and MonteCarlo calculations agree very well during the spatiotemporaltransient process as well as in the new steady state finallyreached.