Excited structures in the Z = 80, 178Hg (N = 98), and 180Hg (N = 100) isotopes have been investigated with the Gammasphere spectrometer in conjunction with the recoil-decay tagging technique. The present data extend the previously known ground-state bands to higher spin and excitation energy. Negative parity bands with a complex decay towards the low spin states arising from both the prolate-deformed and the nearly spherical coexisting minima have been observed for the first time in both nuclei. It is shown that these sequences have characteristics in common with negative-parity bands in the heavier even-even Hg isotopes as well as in the Os and Pt isotones. These structures are interpreted as being associated at low spin with an octupole vibration which is crossed at moderate frequency by a shape driving, two-quasiproton excitation