  This is the first paper of two ones. Here we prove that two compact
Alexandrov surfaces of bounded integral curvature having no peak points are
bi-Lipschitz equivalent if they are homeomorphic one to the other. Also
conditions under that two ends having finite integral negative curvature are
bi-Lipschitz equivalent are considered. In the second paper it is shown that a
bi-Lipschitz constant can be estimated depending on several geometric
characteristics.
