  It is shown that the recently observed Delta J = 2 staggering effect (i.e.
the relative displacement of the levels with angular momenta J, J+4, J+8, ...,
relatively to the levels with angular momenta J+2, J+6, J+10, ...) seen in
superdeformed nuclear bands is also occurring in certain electronically excited
rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is
attributed to interband interactions (bandcrossings). In addition, the Delta J
= 1 staggering effect (i.e. the relative displacement of the levels with even
angular momentum J with respect to the levels of the same band with odd J) is
studied in molecular bands free from Delta J = 2 staggering (i.e. free from
interband interactions/bandcrossings). Bands of YD offer evidence for the
absence of any Delta J = 1 staggering effect due to the disparity of nuclear
masses, while bands of sextet electronic states of CrD demonstrate that Delta J
= 1 staggering is a sensitive probe of deviations from rotational behaviour,
due in this particular case to the spin-rotation and spin-spin interactions.
