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In a multi-gyrotron system such as the one presently designed for the ITER ECH & ECCD system, stray magnetic fields can significantly alter the operational capabilities of the global system. A numerical study was carried out within the European Gyrotron Consortium (EGYC) to assess the importance of the different effects and their impact on the gyrotron operation. Using the Ariadne++ 3D code, and based on the geometrical layout of the ITER-EC system, the effect of the ITER stray magnetic field combined together with the stray field generated by neighboring gyrotrons on the electron beam parameters was considered. It is shown that these effects are important in the gyrotron collector regions in particular for gyrotrons located at the edges of the ITER EC system. The effect of ferromagnetic structure materials was studied using the finite element software package COMSOL Multiphyics. This study was simplified by considering the effect of only one realistic I-beam placed at different distances and orientations with respect to a single gyrotron. It is shown that, with the present geometrical layout of the ITER EC-system, the effects due to ferromagnetic material are negligible.