The aim of radiation tumour therapy is to destruct the tumour whilst sparing the healthy tissue to a large extent. The induction of DNA damage, especially the induction of DNA double strand breaks (DSBs), plays an essential role in the radio-therapeutic treatment of cancer. Carbon beams have achieved growing interest for tumour therapy in the last years and the successful application of heavy ion irradiation in the tumour therapy was shown in the clinical studies (Schulz-Ertner et al. 2004, Tsujii et al. 2007). Their inverse dose profile and extreme precision allows target conformal irradiation while sparing the healthy tissue to a large extent. A special feature of carbon ion tumour therapy is the biological action of the ions with enhanced relative biological effectiveness in the tumour volume. The reduced cell survival (Weyrather et al. 1999) and the decreased repair of DNA-Double Strand Breaks (Heilmann et al. 1996) in the tumour lead to the conclusion that the success of the carbon ion therapy is based on the differences in the quality and the repair of the induced DNA-lesions. In this thesis, the induction and repair of DNA-Double Strand Breaks was measured in the experimental model that simulated the therapeutical carbon ion irradiation of a patient. To study DSBs under conditions mimicking therapeutical ion irradiation, cells were exposed to high energy carbon ions in a water phantom. Human fibroblasts or prostate tumour cells were placed in the entrance channel (healthy tissue) and in the extended Bragg-Peak (tumour) region. The molecular marker γH2AX was used for DSB detection. The γH2AX Foci were imaged in the cells by confocal microscopy. For the quantification of the γH2AX signals a software based, semi-automatic procedure was established. In the region of the healthy tissue, the repair of DNA-lesions was comparable with the results of the photon irradiation which is important for the estimation of the late effects of the therapy with carbon ions. However, in the tumour region the level of residual DSBs was slightly but consistently increased after exposure to Bragg peak ions. The residual, irreparable or very slow reparable DNA-lesions after ion irradiation in the tumour region were further characterized by comparing with the behaviour of γH2AX, 53BP1 and Mre11 foci in track segment experiments using carbon or heavier ions. Irradiation with heavy ions under standard and microbeam conditions induced distinct γH2AX foci. For the later time points (> 2 h after irradiation), we observed splitting of the primary γH2AX foci in sub-compartments or smaller foci. The generated secondary foci were localized in different layers of the nucleus and persisted for several days (for very heavy ions). Colocalization with 53BP1, Mre11, PML and p53 was analysed. The dispersion and splitting of ion induced foci was also detected in live cell imaging experiments with HeLa 53BP1-GFP cells. Furthermore, the localisation of the residual γH2AX signals within the nuclear chromatin structure in HeLa-GFP cells was strongly influenced by the chromatin structure. The data obtained contribute to a better understanding of the spatial "reorganisation" of nuclear lesion processing after induction of DSBs.