1. Ion beam system for irradiating tumour tissues at various irradiation angles (&ggr;) in relation to a horizontally arranged patient couch ( 1 ), characterised in that the patient couch ( 1 ) has an apparatus ( 2 ) for rotation about a vertical axis ( 3 ); and the ion beam system ( 4 ) has at least one of the following irradiation systems: a first irradiation system ( 5 ) having a symmetrical or asymmetrical scanning system ( 6 ) of fixed location, which has a central ion beam deflection region ( 7 ) for deflection angles (&bgr;) of up to ±15° with respect to the horizontal direction and makes possible scanning of a tumour volume in the central ion beam deflection region ( 7 ), and which has an additional lifting apparatus ( 8 ) for the patient couch ( 1 ); a second irradiation system ( 9 ), which has an ion beam deflection apparatus ( 10 ) for a deflection angle (&bgr;) range greater than the first irradiation system ( 5 ) and a symmetrical scanning unit ( 11 ) for scanning the tumour volume, which scanning unit ( 11 ) is arranged downstream of the ion beam deflection apparatus ( 10 ) and is arranged to pivot synchronously with the deflection angle (&bgr;) of the ion beam deflection apparatus ( 10 ).