The theory of hindered rotation of diatomic molecular impurities at cubic sites in ionic crystals is generalized to account for the orbital degeneracy of the molecule, with use of a crystal-field approach. This theory explains the observed <110> orientations of the molecular axis, the orientations of the orbitals along either <110> or <100> axes, and the dominance of 90°tunneling in some cases, even using only the lowest-order term in the octahedral crystal field (l=4). It is shown that the coupling of the degenerate orbital to the rotation in the crystal field generates an instability if the molecular axis is parallel to a <111> direction, leading to a Jahn-Teller effect resulting from rotational-electronic (rotronic) coupling. Analytic expressions for the lowest branch of the adiabatic potential energy as a function of the orientation of the molecular axis are calculated for, and states, and the orbital wave functions are determined for -state molecules. The case of a diatomic molecular impurity at a site of tetrahedral symmetry is discussed.