  Precise energies of rovibrational states of the exotic hydrogen-like molecule
$(dt\mu)Xee$ are of importance for $dt\mu$ resonant formation, which is a key
process in the muon-catalyzed fusion cycle. The effect of the internal
structure and motion of the $dt\mu$ quasi-nucleus on energy levels is studied
using the three-body description of the $(dt\mu)Xee$ molecule based on the
hierarchy of scales and corresponding energies of its constituent subsystems.
For a number of rovibrational states of $(dt\mu)dee$ and $(dt\mu)tee$, the
shifts and splittings of energy levels are calculated in the second order of
the perturbation theory.
