Fundamental research on the harmful effects of ionizing radiation on living cells continues to be of great interest. Recently, priority has been given to the study of high-charge and high-energy (HZE) ions that comprise a substantial part of the galactic cosmic ray (GCR) spectra that would be encountered during long-term space flights. Moreover, predictions of the delayed genetic effects of high linear energy transfer (LET) exposure is becoming more important as heavy ion therapy use is increasing. This work focuses mainly on the basic research on the delayed effects of HZE ions on V79 Chinese hamster cells, with emphasis on the induction of HPRT mutations after prolonged expression times (ET). The research was conducted under various irradiation conditions with accelerated ions O-18 (E = 35.2 MeV/n), Ne-20 (E = 47.7 MeV/n and 51.8 MeV/n), and B-11 (E = 32.4 MeV/n), with LET in the range from 49 to 149 keV/mu m and with Co-60 gamma-rays. The HPRT mutant fractions (MF) were detected in irradiated cells in regular intervals during every cell culture recultivation (every 3 days) up to approximately 40 days (70-80 generations) after irradiation. The MF maximum was reached at different ET depending on ionizing radiation characteristics. The position of the maximum was shifting towards longer ET with increasing LET. We speculate that the delayed mutations are created de novo and that they are the manifestation of genomic instability. Although the exact mechanisms involved in genomic instability initiation are yet to be identified, we hypothesize that differences in induction of delayed mutations by radiations with various LET values are related to variations in energy deposition along the particle track. A dose dependence of mutation yield is discussed as well.