In order to understand the translational and rotational motion in dense molecular liquids, detailed molecular dynamics simulations of Lennard–Jones ellipsoids have been carried out for three different values of the aspect ratio κ. For ellipsoids with an aspect ratio equal to 2, the product of the translational diffusion coefficient (DT) and the average orientational correlation time of the ℓ-th rank harmonics (τlR), converges to a nearly constant value at high density. Surprisingly, this density independent value of DTτlR is within 5% of the hydrodynamic prediction with the slip boundary condition. This is despite the fact that both DT and τlR themselves change nearly by an order of magnitude in the density range considered, and the rotational correlation function itself is strongly nonexponential. For small aspect ratios (κ⩽1.5), the rotational correlation function remains largely Gaussian even at a very large density, while for a large aspect ratio (κ⩾3), the transition to the nematic liquid-crystalline phase precludes the hydrodynamic regime. Thus, the rotational dynamics of ellipsoids show great sensitivity to the aspect ratio. At low density, τlR goes through a minimum value, indicating the role of interactions in enhancing the rate of orientational relaxation.