A syndiotactic alternating ethylene-propylene (SYN-ALT-EP) copolymer was synthesized. Two molecular relaxation processes (alpha and beta relaxations) have been found below room temperature via dynamic mechanical analysis (d.m.a.) : the alpha relaxation at -60 degrees C and the beta relaxation at -125 degrees C. The apparent activation energy of the alpha relaxation is 285 kJ mol(-1), and the activation energy of the beta relaxation is 43 kJ mol(-1) based on the Arrhenius equation. Molecular motion in SYN-ALT-EP copolymer was probed by solid-state C-13 n.m.r. experiments. At temperatures above the glass transition temperature (T-g) there are two major molecular motions in this copolymer : a backbone motion (the rotational motion about single bonds) and a methyl side group rotation. The backbone motion is frozen below T-g, but there is still a methyl rotation. As the temperature is further decreased to about -175 degrees C, well below the beta-transition observed in d.m.a., the methyl side group rotation slows down, suggesting that the methyl rotation may be associated with the observed beta relaxation process.