  Some results on existence of global Chebyshev coordinates on a Riemannian
manifold or, more generally, on Aleksandrov surface are proved. For instance,
if the positive and the negative parts of integral curvature of a Riemannian
manifold M are less than 2\pi each, then there exist global Chebyshev
coordinates on M. These conditions are optimal. Such coordinates help to get
bi-Lipschitz maps between surfaces.}
