Abstract: The level structures of the very neutron-rich nuclei Pd-128 and Pd-126 have been investigated for the first time. In the r-process waiting-point nucleus Pd-128, a new isomer with a half-life of 5.8(8) μs is proposed to have a spin and parity of 8(+) and is associated with a maximally aligned configuration arising from the g(9/2) proton subshell with seniority v = 2. For Pd-126, two new isomers have been identified with half-lives of 0.33(4) and 0.44(3) μs. The yrast 2(+) energy is much higher in Pd-128 than in Pd-126, while the level sequence below the 8(+) isomer in Pd-128 is similar to that in the N = 82 isotone Cd-130. The electric quadrupole transition that depopulates the 8(+) isomer in Pd-128 is more hindered than the corresponding transition in Cd-130, as expected in the seniority scheme for a semimagic, spherical nucleus. These experimental findings indicate that the shell closure at the neutron number N = 82 is fairly robust in the neutron-rich Pd isotopes.