[en] The structure and elastic properties of (5,5) and (10,10) nanotubes, as well as barriers for relative rotation of the walls and their relative sliding along the axis in a double-walled (5,5)-(10,10) carbon nanotube, are calculated using the density functional method. The results of these calculations are the basis for estimating the following physical quantities: ultimate shear strengths and diffusion coefficients for relative sliding along the axis and rotation of the walls, as well as frequencies of relative rotational and translational oscillations of the walls. The commensurability-incommensurability phase transition is analyzed. The length of the incommensurability defect is estimated on the basis of ab initio calculations. It is proposed that a double-walled carbon nanotube be used as a plain bearing. The possibility of experimental verification of the results is discussed