  We describe classes of coordinate systems in Carnot-Carath\'eodory spaces of
low smoothness which allow for homogeneous approximations of quasimetrics and
basis vector fields. We establish the minimal smoothness required for these
classes to coinside with the class of the privileged coordinates described
earlier for the smooth case. We also apply these results to prove partial
analogues of existing results in the canonical coordinates of the 2nd kind. As
a geometric tool we prove some convergence theorems in quasimetric spaces.
