Method for local stabilisation of a beam spot (S) on a remote target object (Z), the beam dot (S) being formed by a high-energy beam (L) which is directed onto the target object (Z) by a high-energy emitter , and the target object (Z) being illuminated by an illuminating beam (B) which is directed onto the target object (Z) by an illumination device ; - a beam (B'), reflected from the target object (Z) illuminated by the illuminating beam (B), being received by an image capture device after passing through an optical path (P) through which the high-energy beam (L) also passes; - the image, captured by the image capture device , of the illuminated target object (Z) or of part of the illuminated target object being analysed by an image processing device and compared with at least one image, generated at a previous time, of the illuminated target object (Z) or of part of the illuminated target object or with an image stored in an object database; - the result of the comparison made in the image processing device being supplied to a filter device and in parallel therewith a fine tracking regulator ; - the filter device predicting the offset of the beam spot (S) from the holding point in the next time interval, using a movement model for the beam spot (S) on the target object (Z) and the result of the comparison made in the image processing device , and generating a filter correction signal, a movement taken into account in the movement model being composed of components of a movement of the target object (Z) and turbulence influences; - the fine tracking regulator compensating any remaining residual errors using the result of the comparison made in the image processing device , and generating a regulator correction signal; - a correction signal (K) being formed from the filter correction signal and the regulator correction signal; and - the correction signal (K) being applied to an optical correction device , which is arranged in the optical path (P) which is jointly passed through by the high energy laser beam (L) and by the reflected beam (B'). - a beam (B'), reflected from the target object (Z) illuminated by the illuminating beam (B), being received by an image capture device after passing through an optical path (P) through which the high-energy beam (L) also passes; - the image, captured by the image capture device , of the illuminated target object (Z) or of part of the illuminated target object being analysed by an image processing device and compared with at least one image, generated at a previous time, of the illuminated target object (Z) or of part of the illuminated target object or with an image stored in an object database; - the result of the comparison made in the image processing device being supplied to a filter device and in parallel therewith a fine tracking regulator ; - the filter device predicting the offset of the beam spot (S) from the holding point in the next time interval, using a movement model for the beam spot (S) on the target object (Z) and the result of the comparison made in the image processing device , and generating a filter correction signal, a movement taken into account in the movement model being composed of components of a movement of the target object (Z) and turbulence influences; - the fine tracking regulator compensating any remaining residual errors using the result of the comparison made in the image processing device , and generating a regulator correction signal; - a correction signal (K) being formed from the filter correction signal and the regulator correction signal; and - the correction signal (K) being applied to an optical correction device , which is arranged in the optical path (P) which is jointly passed through by the high energy laser beam (L) and by the reflected beam (B'). <EOS>