This patent application relates to hybrid and/or single-chain rare-cutting endonucleases, called meganucleases, which recognize and cleave a specific nucleotide sequence, to polynucleotide sequences encoding for said rare-cutting endonucleases, to a vector comprising one of said polynucleotide sequences, to a cell or animal comprising one of said polynucleotide sequences or said rare-cutting endonucleases, to a process for producing one of said rare-cutting endonucleases and any use of the disclosed products and methods. More particularly, this invention contemplates any use of such rare-cutting endonuclease for genetic engineering and gene therapy.