The neutron-rich nuclei 109 Pd and 111Pd were produced as fission fragments following the 30Si + 168Er reaction at a beam energy of 142 MeV. Using the identification based on the coincidences with the complementary fission fragments, the ground state bands in 109Pd and 111Pd were found. They are the only positive-parity bands observed so far in 109Pd and 111 Pd. A band, built on top of the 5/2+ ground state exhibiting ∆I = 1 energy-level staggering was observed in each of these nuclei. Both nuclei of interest, 109Pd and 111 Pd, are suggested to lie in the transitional region of Pd isotopes of maximum γ-softness. The ground states of both nuclei are predicted by TRS calculations to be extremely γ-soft with shallow triaxial minima. The first crossing in the new bands is proposed to be due to an alignment of h211/2 neutrons.