$^{13}C$ spin-lattice relaxation times were measured for n-alkanes of moderate chain length, ranging from n-octane to n-dodecane, under the condition of proton broad-band decoupling within the temperature range of 248-318 K in order to gain some insight into basic features of segmental motions occurring in long chain ploymeric molecules. The NOE data showed that except for methyl carbon-13 dipole-dipole interactions between $^{13}C$ and directly bonded $^1H$ provide the major relaxation pathway, and we have analyzed the observed $T_1data$ on the basis of the internal rotational diffusion theory by Wallach and the conformational jump theory by London and Avitabile. The results show that the internal rotational diffusion constants about C-C bonds in the alkane backbone are all within the range of $10^9;-10^10;sec^{-1}$ in magnitude while the mean lifetimes for rotational isomers are all of the order of $10^{-11};-10^{-10}$ sec. Analysis by the L-A theory predicts that activation energies for conformational interconversion between gauche and trans form gradually increase as we move from the chain end toward the central C-C bond and they are within the range of 2-4 kcal/mol for all the compounds investigated.