The understanding of flux jumps in the high temperature superconductors is of importance since the occurrence of these jumps may limit the perspectives of the practical use of these materials. In this work, we present the experimental study of the role of heavy ion irradiation in stabilizing the HTSC against flux jumps by comparing un-irradiated and 7.5 x 10(10) Kr ion/cm(2) irradiated (YxTm1-x)Ba2Cu3O7 single crystals. Using pulsed field magnetization measurements, we have applied a broad range of field sweep rates from 0.1 to 1800 T/s to investigate the behavior of the flux jumps. The observed flux jumps, which may be attributed to thermal instabilities, are incomplete and have different amplitudes. The flux jumps strongly depend on the magnetic field, on the magneto-thermal history of the sample, on the magnetic field sweep rate, on the critical current density j(c), on the temperature and on the thermal contact with the bath in which the sample is immersed. (C) 2000 Elsevier Science B.V. All rights reserved.