  We introduce a Monte Carlo space-time model for high-energy collisions with
nuclei, involving the dynamical interplay of perturbative QCD parton production
and evolution, with non-perturbative parton-cluster formation and `afterburner'
cascading of formed pre-hadronic clusters plus hadron excitations. This
approach allows us to trace the space-time history of parton and hadron degrees
of freedom of nuclear collisions on the microscopical level of parton and
hadron cascades in both position and momentum space, from the instant of
nuclear overlap to the final yield of particles. In applying this approach, we
analyze Pb+Pb collisions at the CERN SPS with beam energy 158 GeV (sqrt{s}/A =
17 GeV) and Au+Au collisions at RHIC with collider energy \sqrt{s}/A = 200 GeV.
We find that the perturbative QCD parton production and cascade development
provides an important contribution to particle production at central
rapidities, and that the `afterburner' cascading of pre-hadronic clusters and
formed hadrons emerging from the parton cascade is essential. The overall
agreement of our model calculations including the `afterburner' cascading with
the observed particle spectra at the CERN SPS is fairly good, whereas the
neglect of the final-state interactions among hadronic excitations deviates
significantly.
