We report µSR experiments carried out on a series of heavy-electron pseudobinary compounds U(Pt_1-xPd_x)₃ (x0.05). For x0.005 the zero-field muon depolarization is described by the Kubo-Toyabe function. However the temperature variation of the Kubo-Toyabe relaxation rate _KT(T) does not show any sign of the small-moment antiferromagnetic phase with T_N6 K (signalled by neutron diffraction), in contrast to previous reports. The failure to detect the small ordered moment suggests it has a fluctuating (>10 MHz) nature, which is consistent with the interpretation of NMR data. For 0.01 x0.05 the muon depolarization in the ordered state is described by two terms of equal amplitude: an exponentially damped spontaneous oscillation and a Lorentzian Kubo-Toyabe function. These terms are associated with antiferromagnetic order with substantial moments. The Knight shift measured in a magnetic field of 0.6 T on single-crystalline U(Pt_0.95Pd_0.05)₃ in the paramagnetic state shows two signals for Bc, while only one signal is observed for Bc. The observation of two signals for Bc, while there is only one muon localization site (0,0,0), points to the presence of two spatially distinct regions of different magnetic response.