We perform self-consistent electronic-structure calculations to investigate the possible existence and formation mechanism of local magnetism in isolated late-4d transition-metal impurities in Pd and dilute Pd-Fe alloys, using the local-spin-density approximation and the cluster model for simulating the bulk. We find that Ru in Pd exhibits a giant moment of 4μ B , but reduced in magnitude compared to its 3d counterpart Fe in Pd. Tc and Rh in Pd turn out to be nonmagnetic, the latter in disagreement with time-differential perturbed-angular-correlation (TDPAC) experiments, which suggest a reduced giant moment per Rh atom also