We measured longitudinal and transverse relaxation times (T(1) and T(2)) for (1)H, (13)C-T(1) and (13)C spectra for room-temperature ionic liquids of 1-alkyl-3-methylimidazolium bromide [C(n)mim]Br (n = 2, 3, 4) as a function of temperature. Their values and spectra reveal close relationships between their unique phase behaviours and the dynamics of carbons constituting the cations. Carbons in these cations are classified into groups according to their dynamics, namely imidazolium carbons, an N-methyl carbon, a terminal methyl carbon of the alkyl group and others of the alkyl group. The temperature dependences of T(1) values for these groups differ greatly, resulting in a variation in the characteristic thermal behaviours of the salts. Values of (1)H-T(1) and (13)C-T(1) suggest that some carbons continue to move even in the crystalline and/or solid states. Using (13)C-T(1) data, we also estimated the temperature dependences of the correlation times for the segmental motions of carbons in the liquid states.