A hydrodynamic model is presented to describe fully anisotropic rotational dynamics of asymmetric ellipsoids in liquids. The model by Gierer and Wirtz is extended to deal with anisotropic rotations and combined with the model by Youngren and Acrivos for slip boundary conditions. The combined model is applied to obtain the reorientational correlation times for the hydrocarbon 5,6-dimethyl-1,2,3,4-tetrahydro-1,4-methanonaphthalene in different solvents. The results from these calculations are compared to experimental values from C-13 nuclear relaxation data. Calculated and experimental results agree very well, and the new combined model is believed to represent an important contribution for describing rotational molecular dynamics in liquids.