  We have performed a molecular dynamics computer simulation of a supercooled
binary Lennard-Jones system in order to compare the dynamical behavior of this
system with the predictions of the idealized version of mode-coupling theory
(MCT). By scaling the time $t$ by the temperature dependent $\alpha$-relaxation
time $\tau(T)$, we find that in the $\alpha$-relaxation regime $F(q,t)$ and
$F_s(q,t)$, the coherent and incoherent intermediate scattering functions, for
different temperatures each follows a $q$-dependent master curve as a function
of scaled time. We show that during the early part of the $\alpha$-relaxation,
which is equivalent to the late part of the $\beta$-relaxation, these master
curves are well approximated by the master curve predicted by MCT for the
$\beta$-relaxation. This part is also fitted well by a power-law, the so-called
von Schweidler law. We show that the effective exponent $b'$ of this power-law
depends on the wave vector $q$ if $q$ is varied over a large range. The early
part of the $\beta$-relaxation regime does not show the critical decay
predicted by MCT. The $q$-dependence of the nonergodicity parameter for
$F_{s}(q,t)$ and $F(q,t)$ are in qualitative agreement with MCT. On the time
scale of the late $\alpha$-relaxation the correlation functions show a
Kohlrausch-Williams-Watt behavior (KWW). The KWW exponent $\beta$ is
significantly different from the effective von Schweidler exponent $b'$. At low
temperatures the $\alpha$-relaxation time $\tau(T)$ shows a power-law behavior
with a critical temperature that is the same as the one found previously for
the diffusion constant [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. The critical
exponent of this power-law and the von Schweidler exponent $b'$ fulfill the
connection proposed by MCT between these two quantities. We also show that the
