In positioning or aligning ends of optical fibers in relation to each other an offset distance between the fiber ends, the offset distance e.g. being the distance between predetermined reference positions in the fiber ends, is stepwise adjusted using a cascade technique. The method can be executed accurately and fast and be used e.g. in a procedure for core alignment, the predetermined reference positions then being the positions of the cores of the fiber ends such as the positions of the center lines or axes of the cores. Also, the method can be used in a procedure in which the self-focusing effect of optical fibers is used for finding the reference positions, which in this case are the positions of the center lines or axes of the total fiber ends, i.e. center lines or axes of the surfaces of the claddings of the optical fiber ends. Finally, the method can be used for the longitudinal positioning of the fiber ends in which the gap between end surfaces of the fiber ends is set to a desired value.