Abstract: A method of aligning two optical fiber ends so that they abut at their frontal faces and light that is fed into one of the two optical fibers is coupled over into the other optical fiber with the least amount of attenuation. A manipulator moves the optical fiber end it holds step-wise in the direction of its longitudinal axis (z) toward the other fiber end and after each step the manipulator is displaced transversely. The change in the coupled-over light power (P) is recorded as a function of transverse displacement and the displacement of the manipulator in the longitudinal direction is stopped as soon as a position (z.sub.0) is reached in which transverse displacement of the manipulator no longer produces a change in the coupled-over lightpower (P).