Classification scheme for double-wall carbon nanotubes (DWCNT) based on their symmetry is proposed. According to the scheme each DWCNT ascribes to a family of DWCNTs with the same geometrical parameters: interwall distance, nanotube unit cell length and difference of wall chirality angles. This geometrical parameters, the barriers for the relative rotation of the wall, sliding along the nanotube axis and helical line of 'thread' and threshold forces causing the relative motion of the walls are calculated for a set of DWCNTs. The results of calculations allow to select DWCNTs that can be used in mechanical nanodevices such as nanobearings and of bolt-and-nut pairs. Possibility of orientational melting of DWCNTs with commensurate walls is discussed. (C) 2003 Published by Elsevier B.V.