Abstract The compounds Ce 3 Pd 20 X 6 ( X = Ge , Si ) manifest unusual physical properties which would catalogue them as magnetic Kondo systems. Our zero-field μ SR measurements were undertaken to gain information about the magnetic behaviour at low temperatures. The muon spin relaxation rate was found to increase up to value of 4 μ s - 1 at 50 mK. Below 0.3 K an increase in the depolarization rate is believed to represent the development of quasi-static ordering of magnetic moments of electronic origin. A follow-up series of transverse-field μ SR measurements were performed. The external fields were varied up to 5 kOe and the temperature dependence of the internal magnetic field was found to be similar to that found in Ce 3 Pd 20 Si 6 . The μ SR experiments were carried out at the PSI, Villigen, Switzerland.