A. D. Alexandrov's Problem for CAT(0)-Spaces

We solve the well-known problem by A. D. Alexandrov for nonpositively curved spaces. Let X be a geodesically complete locally compact space nonpositively curved in the sense of Alexandrov and connected at infinity. The main theorem reads as follows: Each bijection f : X → X such that f and the inverse f ^?1 of f preserve distance 1 is an isometry of X.