High spin states of 80Rb are studied via the fusion-evaporation reactions 65Cu+19F, 66Zn+18O and 68Zn+16O with the beam energies of 75 MeV, 76 MeV and 80 MeV, respectively. Twenty-three new states with twenty-eight new gamma transitions were added to the previously proposed level scheme, where the second negative-parity band is significantly pushed up to spins of 22^{-} and 15^{-} and two new sidebands are built on the known first negative-parity band. Two successive band crossings with frequencies 0.51 MeV and 0.61 MeV in the alpha=0 branch as well as another one in the alpha=1 branch of the second negative-parity band are observed for the first time. Signature
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