The detailed investigation of the local mobility in a set of dried imidazolium-based ionic liquids (1-butyl-3-methylimidazolium) in a wide temperature range and varying anions (BF ₄ ^- , I ^- , Cl ^- , Br ^- , NO ₃ ^- , TfO ^- ) is presented. The measurements of temperature dependencies of the spin-lattice relaxation times of ¹ H and ¹³ C nuclei are motivated by the need to obtain a fundamental characterization of molecular mobility of the substances under study, namely, to estimate the correlation times, τ _c , for the motion of individual molecular groups. In particular, it follows from obtained results that the mobility of the hydrocarbon "tail" is higher (smaller τ _c ) than that of the imidazole ring, and this expected tendency is quantified. The effect of the influence of an anion type on the cation mobility is also analyzed.