We have measured temperature (T )-and power-dependent electron spin resonance in bulk single-wall carbon nanotubes to determine both the spin-lattice and the spin-spin relaxation times, T 1 and T 2 . We observe that T −1 1 increases linearly with T from 4 K to 100 K, whereas T −1 2 decreases by over a factor of two when T is increased from 3 K to 300 K. We interpret the T −1 1 ∝ T trend as spin-lattice relaxation via interaction with conduction electrons (Korringa law) and the decreasing T dependence of T −1 2 as motional narrowing. By analyzing the latter, we find the spin hopping frequency to be 285 GHz. Last, we show that the Dysonian line shape asymmetry follows a three-dimensional variable-range hopping behavior from 3 K to 20 K; from this scaling relation, we extract a localization length of the hopping spins to be ∼100 nm. Understanding spin dynamics is key to a broad range of modern problems in condensed-matter physics 1-6 and applied sciences. 7,8 Spin transport is a sensitive probe of many-body correlations as well as an indispensable process in spintronic devices. Confined spins, particularly those in one dimension (1D), are predicted to show strong correlations 2,4-6,9 and long coherence times.3 Single-wall carbon nanotubes (SWCNTs) are ideal materials for studying 1D spin physics due to their long mean free paths and relatively weak spin-orbit coupling.10 Exotic spin properties in metallic SWCNTs at low temperatures and high magnetic fields have been predicted, including the appearance of a peak splitting in the spin energy density spectrum, which can be used to probe spin-charge separation in Luttinger-liquid theory. [4][5][6] One method for studying spin dynamics is electron spin resonance (ESR), which can provide information on spin-orbit coupling, phase relaxation time, spin susceptibility, and spin diffusion. Many ESR studies of SWCNTs have been performed over the past decade. 5,6,[11][12][13][14][15][16][17][18][19][20][21][22] Unfortunately, substantial conflicts have emerged in the literature, such as the temperature (T ) dependence of the spin susceptibility 12,15,18,22 and whether the ESR is caused by SWCNT defects 11,15,17,21,22 or is intrinsic to nanotubes. 12,13,16,[18][19][20] Because of these divergent empirical observations of nanotube ESR, there is only scant experimental data on electron spin-lattice relaxation times in SWCNTs, which limits our understanding of nanotube spin dynamics.Here, we present a detailed study of the T dependence of both the spin-lattice (T 1 ) and spin-spin (T 2 ) relaxation times of paramagnetic electron spins in SWCNTs. From the T dependence of T 1 , we find that the spin-lattice relaxation rate, T −1 1 , is proportional to T . This trend is consistent with the notion that the probed spins relax through interaction with conduction electrons that are present in metallic SWCNTs in the sample. Additionally, we find that the dephasing rate, T −1 2 , becomes smaller as T is increased, which is a hallmark of the phenomenon of motional narrowing. 23,24 This spin...