© 2019 The Author(s) 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 125 Pd 79 and 127 Pd 81 studied using the EURICA γ-ray spectrometer, following production via in-flight fission of a high-intensity 238 U 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 125 Pd and 127 Pd, 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 132 Sn.