A modified Dunham potential with parameters depending on the rotationa
l quantum number is employed to describe the rovibrational states of d
iatomic molecules. This approach, applied to (HBr)-Br-81, (InD)-In-115
, (LiH)-Li-7, and Ar-40(2), gives satisfactory reproduction of the obs
erved transitions using fewer Dunham parameters than in the standard m
ethod. The results obtained indicate the possibility of introducing th
e local internal potentials, which, in contradiction to the global one
s usually used, depend on the rotational states of a rotating-vibratin
g molecule. Such a J dependence may be a result of rovibronic interact
ions, in particular, Coriolis-type nonadiabatic interactions coupling
other electronic states through the rotational angular momentum.