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

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... 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 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 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 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) C_l^(s)(t) F_s(q,t) for all m.