Abstract : The neutron-rich nuclei 109Pd and 111Pd were produced as fission fragments following the 30Si+168Er reaction at 142 MeV. Using the identification based on the coincidences with the complementary fission fragments, the only positive-parity bands observed so far in 109Pd and 111Pd emerged from this work. A band, built on top of the 5/2+ ground state exhibiting ΔI=1 energy-level staggering, was observed in each of these nuclei. Both nuclei of interest, 109Pd and 111Pd, are suggested to lie in the transitional region of Pd isotopes of maximum γ softness. The ground states of both nuclei are predicted by total Routhian surface calculations to be extremely γ soft with shallow triaxial minima. The first crossing in the new bands is proposed to be attributable to an alignment of h11/22 neutrons.