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A self-consistent model of the spatial structure and dynamics of the pulsed direct current (DC) oxygen discharge in oxygen at low pressures has been developed. The dynamics of the electrons in the discharge and in the afterglow have been calculated on the base of the PIC MC method and the diffusion-drift approach correspondingly. As a result, nonlocality and anisotropy effects of the electron energy distribution function (EEDF) which are of primary importance in strongly nonuniform electric field have been taken into account. Spatial distributions of charged and neutral species were determined in the diffusion-drift approach. The processes in the active phase of the discharge were found to be essentially transient. The densities of positive and negative ions as well as the EEDF significantly vary during the discharge pulse, although the discharge current density remains approximately constant. The evolution of the EEDF in the discharge is mainly determined by degradation of the beam of γ-electrons from the cathode and therefore has a clearly pronounced two-temperature character. The high density of slow electrons produced by beam electrons is the principal condition for negative ion production by the dissociative attachment of these slow electrons to highly excited oxygen molecules in the Herzberg's states A3Σu+,A'3Δu,c1Σu- both in the discharge and in the afterglow. To prove out the presence of high density of slow electrons in the discharge, a special experiment using a high-precision measurement of the EEDF in oxygen DC discharge stimulated by a beam of runaway electrons was carried out. The good agreement between these measurements and our simulation results indirectly confirms a two-temperature character of the EEDF in a pulsed DC oxygen discharge at low pressures.