We report dc and ac magnetization of the newly discovered Cd-Mg-RE quasicrystals (RE = Gd, Tb, Dy, Ho, Er, Tm and Yb). For all the RE atoms except Yb, the temperature dependence of the dc magnetization obeys the Curie-Weiss law at higher temperatures, T>50 K. Estimated effective moments indicate that these atoms are in the trivalent states. In contrast, the Cd-Mg-Yb quasicrystal shows very small magnetization, suggesting that Yb is in the non-magnetic divalent state. At lower temperatures, spin-glass-like freezing was observed for the RE atoms except Tm and Yb. In particular, the freezing proceeds in two successive steps for RE = Gd, Tb, Dy and Ho, being quite different from canonical spin-glasses.