  Using molecular dynamics computer simulations we study the dynamics of a
molecular liquid by means of a general class of time-dependent correlators
S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational
degrees of freedom (ODOF). The system is composed of rigid, linear molecules
with Lennard- Jones interactions. The q-dependence of the static correlators
S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are
calculated for l=l'. A thorough test of the predictions of mode coupling theory
(MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for
l=1,..,6. We find a clear signature for the existence of a single temperature
T_c, at which the dynamics changes significantly. The first scaling law of MCT,
which involves the critical correlator G(t), holds for l>=2, but no critical
law is observed. Since this is true for the same exponent parameter lambda as
obtained for the TDOF, we obtain a consistent description of both, the TDOF and
ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1
can also be seen from the corresponding susceptibilities
(chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency
omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega)
for which omega'_{min} approx 10 omega_{min} . The asymptotic regime, for which
the first scaling law holds, shrinks with increasing l. The second scaling law
of MCT (time-temperature superposition principle) is reasonably fulfilled for l
\ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of
the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong
C_l^{(s)}(t) F_s(q,t) for all m.
