Octupole correlations in superdeformed high-spin states

Recent theoretical works done by us on the following subjects are briefly summarized: 1) Octupole vibrations with K=0, 1, 2 and 3 built on superdeformed yrast states, 2) Octupole vibration-quasiparticle couplings in superdeformed odd-A nuclei, 3) Supershell structure in superdeformed nuclei which break the reflection symmetry, 4) Analysis of the supershell effects in terms of semiclassical theory of quantum level density. An intimate relationship among octupole instability of the superdeformed shape, the rise of supershell effects, and bifurcations of classical periodic orbits is suggested.