We have carried out 121,123Sb nuclear quadrupole resonance (NQR) measurements on ReRu4Sb12 (Re = La, Ce and Pr) to investigate an anomalous behavior of the nuclear spin-echo relaxation rate 1/T2 observed in ReOs4Sb12. The full width at half maximum of the NQR spectrum shows a step-like increase below 130 K with decreasing temperature. Temperature dependence of 1/T2 also shows a divergence at ∼115 K whereas the nuclear spin-lattice relaxation rate 1/T1 does not show any anomaly. These results are caused by a distribution of the electric field gradient (EFG) and its fluctuations, which might arise from a rattling motion of the rare earth ion centered in the cage which consists of twelve Sb and/or a small deformation of the cage. The EFG fluctuations observed in ReOs4Sb12 and ReRu 4Sb12 at T ∼ 120 K originates from an unique crystal structure of the filled skutterudite with oversized Sb-cage. © 2011 The Physical Society of Japan.