Local f-electron spin dynamics in the non-Fermi-liquid heavy-fermion alloys UCu_{5-x}Pd_x, x = 1.0 and 1.5, have been studied using muon spin-lattice relaxation. The sample-averaged asymmetry function Gbar(t) indicates strongly inhomogeneous spin fluctuations, and exhibits the scaling Gbar(t,H) = Gbar(t/H^gamma) expected from glassy dynamics. At 0.05 K gamma(x=1.0) = 0.35 pm 0.1, but gamma(x=1.5) = 0.7 pm 0.1. This is in contrast to inelastic neutron scattering results, which yield gamma = 0.33 for both concentrations. There is no sign of static magnetism gtrsim 10^{-3} mu_B/U ion in either material above 0.05 K. Our results strongy suggest that both alloys are quantum spin glasses.
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