We investigate in self-consistent cranked Nilsson plus quasiparticle random-phase approximation the structure of 190,192,194Hg in their evolution from normal to superdeformation and from low to high rotational frequencies. The analysis of the energy levels suggests a splitting of few normally deformed bands into two or more branches. The investigation of the dynamical moments of inertia supports the octupole character of the low-lying negative parity superdeformed bands, in agreement with previous theoretical predictions and experimental findings. As a more direct confirm of their octupole nature, we obtain strong E1 transitions linking those bands to the yrast superdeformed band, in agreement with experiments. A similar result is shown to hold also for 152Dy. Like in 152Dy, the collectivity of the low-lying scissors mode gets enhanced with the onset of superdeformation