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Rotational and translational diffusion of the series of stable nitroxide radicals in nematic and smectic mesophases was investigated by means of EPR spectroscopy. Characteristics of rotational mobility of the radicals were estimated by numerical simulation of the shape of their EPR spectra. It was found that mechanism of rotation of the probes in liquid crystals is essentially differs from rotation in unstructured matrixes and can not be described as Brownian diffusion. Radicals with sufficiently nonaxial inertia properties rotate fast around one axis and vibrate around perpendicular ones. Also it was shown that chemically identical admixture molecules in liquid crystal matrices can have different rotational properties. Rotation diffusion coefficients for such particles can differ by an order of magnitude. This fact indicates various localization of admixture molecules in liquid crystalline media. Coefficients of translational diffusion of the radicals were found by analysis of concentration broadening of EPR spectra reflecting their spin exchange interactions. The results are compared with the data obtained by other methods.