High spin states in the N=79 Ce-137 nucleus have been studied with the reac
tion Sn-124(O-18, 5n)Ce-137 at beam energy 78 MeV. The level scheme has bee
n expanded with spin up to 43/2 (h) over bar. At low spins, the yrast colle
ctive structure built on the nu h(11/2)(-1) x 2(+) multiplet shows a transi
tional shape with gamma = 30.8 degrees according to calculations of the tri
axial rotor-plus-particle model. The configurations for several high spin s
tates have been discussed from a systematical comparison with neighboring n
uclei. A collective band built on I = 33/2 level has been observed for the
first time. This band has an oblate shape with gamma = -60 degrees and most
probably originates from the five-quasiparticle nu s(1/2) x [nu h(11/2)] x
pi g(7/2) x pi h(11/2) configuration.