Aboard INTEGRAL, the next medium-size γ-ray mission of the European Space Agency (ESA), a high-resolution Ge-spectrometer array with a BGO anticoincidence shield and imaging capability will be flown. The influence of the radiation damage on the photoelectron yield of the BGO scintillators due to the radiation environment in the orbit, i.e. γ-rays, electrons and protons from the radiation belts and the cosmic diffuse radiation, was investigated. Irradiation tests with doses equivalent to the orbit conditions were performed and the photoelectron yields of different BGO crystals were measured. It was found that for equal doses the reduction of the photoelectron yield varies strongly for the crystals of different manufacturers. Furthermore, electromagnetic radiation affects the photoelectron yield much stronger than particle radiation. A possible explanation is given by interpreting the effect due to γ-rays primarily as damage of the electronic structure of the BGO, whereas the particle radiation damages mainly the crystal structure.