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Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classification of the symmetry types of relative equilibria of AB[sub 2] molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D[sub 2] H[sup +] and H[sub 2] D[sup +] . These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H[sub 2] D[sup +] from J 26. [ABSTRACT FROM AUTHOR]