A method and device to stabilize the cornea with fewer adverse effects. In particular, a greater stability and shorter treatment time are to be made possible. To this end, the cornea is locally irradiated successively at different sites so that collagen fibers are indirectly or directly crosslinked at the irradiated sites. In this way, the collagen fibers are advantageously crosslinked in a spatially resolved manner. Accordingly, the entire eye need not be irradiated with tissue-damaging UV light, and regions having a weaker structure can be locally stabilized selectively. The sites of the cornea are preferably irradiated so that the collagen fibers are ionized in each instance by photoabsorption of a plurality of photons which each have an energy below an ionizing energy of a given molecule. After a short treatment period, strong covalent bonds are formed directly between the collagen fibers. Crosslinking agents need not be used.
