A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd 2/3 Ca 1/3 MnO 3 perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T g ~ 60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole-Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at "macroscopic" time scale. Slow relaxation in the zerofield-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T g , associated with its antiferromagnetic-ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T g and above it are strongly different. Magnetic field up to about m 0 H ~ 0.4 T suppresses the glassy magnetic state of the compound.