The collective properties of excited superdeformed bands have been investigated in the framework of self-consistent cranked Nilsson plus quasiparticle random-phase approximation. The expected octupole nature of some bands observed recently in some nuclei has been confirmed by a comparative analysis of their E1 decays to the yrast band and of the anomalous behavior of their dynamical moment of inertia. It is also shown that the onset of supederformation affects considerably the structure of the giant resonances and greatly enhances the collectivity of the low-lying scissors mode.