This thesis focuses on radiation degradation studies of polyimide, polyepoxy/glass-fiber composites and other technical components used, for example, in the superconducting magnets of new ion accelerators such as the planned International Facility for Antiproton and Ion Research (FAIR) at the GSI Helmholtz Center of Heavy Ion Research (GSI) in Darmstadt. As accelerators are becoming more powerful, i.e., providing larger energies and beam intensities, the potential risk of radiation damage to the components increases. Reliable data of the radiation hardness of accelerator materials and components concerning electrical, thermal and other technical relevant properties are of great interest also for other facilities such as the Large Hadron Collider (LHC) of CERN. Dependent on the position of the different components, induced radiation due to beam losses consists of a cocktail of gammas, neutrons, protons, and heavier particles. Although the number of heavy fragments of the initial projectiles is small compared to neutrons, protons, or light fragments (e.g. α particles), their large energy deposition can induce extensive damage at rather low fluences (dose calculations show that the contribution of heavy ions to the total accumulated dose can reach 80 %). For this reason, defined radiation experiments were conducted using different energetic ion beams (from protons to uranium) and gamma radiation from a Co-60 source. The induced changes were analyzed by means of in-situ and ex-situ analytical methods, e.g. ultraviolet-visible and infrared spectroscopy, residual gas analysis, thermal gravimetric analysis, dielectric strength measurements, measurements of low temperature thermal properties, and performance tests. In all cases, the radiation induces a change in molecular structure as well as loss of functional material properties. The amount of radiation damage is found to be sensitive to the used type of ionizing radiation and the long term stability of the materials is discussed within the focus of its application.