The radiation stability of plastic scintillators and wavelength shifters for the calorimeter of the ZEUS detector has been investigated by irradiating them with protons, a /sup 60/Co source, and depleted uranium. Changes in light yield, absorption length, and absorption coefficient have been measured for storage in inert and oxygen atmospheres during and after irradiation. Radiation doses of up to 40 kGy with dose rates of 30 to 2000 Gy/h have been applied. The polystyrene-based scintillator SCSN-38 and the wavelength shifters Y-7 and K-27 in PMMA (polymethyl methacrylate) initially show a strong additional absorption but then recover in air to a low permanent damage (at 10 kGy) which is proportional to the applied dose. Series investigations on samples of all production cycles of the ZEUS scintillators at high dose rates show only minor differences in radiation hardness.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>