Abstract: The neutron-rich isotopes of palladium have attracted considerable interest in terms of the evolution of the N = 82 neutron shell closure and its influence on the r-process nucleosynthesis. In this Letter, we present the first spectroscopic information on the excited states in Pd-125(79) and Pd-127(81) studied using the EURICA gamma-ray spectrometer, following production via in-flight fission of a high-intensity U-238 beam at the RIBF facility. New isomeric states with half-lives of 144(4) ns and 39(6) μs have been assigned spins and parities of (23/2(+)) and (19/2(+)) in Pd-125 and Pd-127, respectively. The observed level properties are compared to a shell-model calculation, suggesting the competition between proton excitations and neutron excitations in the proton-hole and neutron-hole systems in the vicinity of the doubly magic nucleus Sn-132.