  We present a nonperturbative dynamical study of $e^+e^-$ production in
proton-nucleus and nucleus-nucleus collisions from AGS to SPS energies on the
basis of the covariant transport approach HSD. For p + Be reactions the
dilepton yield for invariant masses $M \leq 1.4$ GeV is found to be dominated
by the decays of the $\eta, \rho, \omega$ and $\Phi$ mesons at all energies
from 10 -- 450 GeV. For nucleus-nucleus collisions, however, the dilepton yield
shows an additional large contribution from $\pi^+\pi^-$, $K^+K^-$ and $\pi
\rho$ channels. Systematic studies are presented for the 'free' meson mass
scenario in comparison to a 'dropping' meson mass scenario at finite baryon
density. We find that for 'dropping' meson masses the invariant dilepton mass
range 0.35 GeV $\leq M \leq$ 0.65 GeV is increased in comparison to the 'free'
meson mass scenario and that the data of the CERES-collaboration for
nucleus-nucleus collisions can be described much better within the 'dropping'
mass scheme. We study in detail the contributions from the various dilepton
channels as a function of the transverse momentum and rapidity of the lepton
pair as well as a function of the charged particle multiplicity. Furthermore,
various direct photon channels for S + Au at 200 GeV/u are computed and found
to be well below the upper bounds measured by the WA80-collaboration.
