Using the GAMMASPHERE array in conjunction with the Fragment Mass Analyzer,
the level structure of the near drip-line nucleus Hg-178 has been consider
ably expanded with the recoil-decay tagging technique. Of particular intere
st is a new rotational band which exhibits a complex decay towards the low
spin states arising from both the prolate-deformed and the nearly spherical
coexisting minima. It is proposed that this band is associated at low spin
with an octupole vibration which is crossed at moderate frequency by a sha
pe driving, two quasiproton excitation.