The UCu_5-xPd_x heavy-fermion alloy system is known to exhibit non-Fermi-liquid (NFL) behaviour for compositions with x1. The magnetic properties associated with NFL behaviour of this system are the focus of this study. Results are presented on the temperature (1.7 T300 K) and magnetic field (0 B5 T) dependences of the magnetization M and susceptibility for polycrystalline UCu_5-xPd_x samples with x = 0.8, 0.9, 1.0 and 1.2. We emphasize the observed field dependence of at low temperatures and illustrate the instability of NFL properties against magnetic field. Our (T) data present a systematic power-law divergence for NFL UCu_5-xPd_x at low temperatures in the limit of small measuring fields. This is interpreted in terms of Griffiths-phase singularities near a quantum critical point which are treated in a model given by Castro Neto and co-workers that includes the effects of structural disorder and a generic RKKY-Kondo interplay (where RKKY Ruderman-Kittel-Kasuya-Yosida). For the extended range 1.7 T300 K, we find that (T) scales reasonably well with a theoretical expectation of Souletie and co-workers of NFL behaviour of Kondo systems. Finally, our M(T,B) data for magnetic fields up to 5 T and 1.7 T21 K are shown to conform to a NFL scaling relation that applies to T = 0 quantum critical systems. The above analyses support the role that magnetic interactions are thought to play in NFL UCu_5-xPd_x.