An extensive study of both H-1 and C-13 T-1 (spin-lattice) and T-1 rho (spin-lattice in the rotating frame) relaxation times as well as T-CH (proton-carbon cross-polarisation times) was undertaken in order to investigate the morphology and dynamics of an ethylene/propylene/ethylidene-norbornene terpolymer and two ethylene/propylene random copolymers obtained using different catalytic systems. Several selective n.m.r. techniques were first used in order to obtain information on the structure and phase composition of the three copolymers. Two of the samples were found to consist of a single phase, whereas the copolymer obtained with a Ti-based catalyst clearly showed three phases : rubbery ethylene/propylene random copolymer, crystalline polyethylene, and isotactic crystalline polypropylene. Moreover, a fourth phase, made of ’rigid’ amorphous polyethylene, bordering the crystalline polyethylenic regions, was singled out by means of H-1 T-1, C-13 T-1 rho and T-CH measurements. In the same sample the dimensions of the crystalline domains dispersed in the rubber matrix were roughly estimated on the basis of the proton relaxation times. Qualitative and semi-quantitative information on motions in the kHz and MHz ranges was derived from carbon relaxation times.