  We calculate the nonadiabatic relativistic correction to rovibrational energy
levels of H$_2$, D$_2$, and HD molecules using the nonadiabatic perturbation
theory. This approach allows one to obtain nonadiabatic corrections to all the
molecular levels with the help of a single effective potential. The obtained
results are in very good agreement with the previous direct calculation of
nonadiabatic relativistic effects for dissociation energies and resolve the
reported discrepancies of theoretical predictions with recent experimental
results.
