In this report, we present and discuss new results for NQR and muSR experiments in CeCu6-xAux, for x=0.3 (Neel temperature TN about 0.5 K) and x = 0.8 (TN about 1.8 K), carried out as part of our study of the spin dynamics, the magnetic ground-state and precursor effects on approaching TN. In these compounds the NQR relaxation rate for T>>TK (the Kondo temperature) is consistent with a relaxation process driven by screened local Ce moments with a weak temperature and x dependence on cooling. The low temperature effective screening increases with decreasing x. The low-temperature zero-field muSR reveals an enhanced relaxation rate that does not appear to follow a critical law, as expected on approaching the ordering temperature.