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A relativistic kinetic formulation of the time evolution of parton distributions during the early preequilibrium stage of nucleus-nucleus collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) is presented to study the microscopic dynamics and equilibration of the system. The nuclear collision is described as a sequence of multiple hard and soft parton-parton collisions and associated parton emission and absorption processes. Important aspects for the space-time evolution of the partonic system are the balance between emissive and absorptive processes, dilated formation of gluon radiation, and the effects of soft gluon interference. The time evolution of central 32S+32S and 1 9 7 A~+ 1 9 7 A~ collisions at RHIC (fi = 200A GeV) is studied in complete phase space and the approach to equilibrium is investigated. The results obtained imply the formation of hot quark-gluon plasmas in these collisions with estimated equilibration times, temperatures, and energy densities of re, ~1 . 2 (1.8) fm/c, T 2.290 (325) MeV, and E ~1 7 (31) Gev/fm3 for 3 2~+ 3 2~ (197A~+197A~). The consequences of such rather high temperatures and energy densities should be clear quark-gluon plasma signatures, observable in the production of charm, strangeness, direct photons, and dileptons. PACS number(s): 25.75. +1, 12.38.Bx, 12.38.Mh, 24.85.f~