A combined PET/MRI tomography unit has a PET unit with a unit part assigned to the examination space, and a first evaluation unit for evaluating the PET electric signals. The unit part has a gamma ray detector. The combined unit has an MRI unit and a second evaluation unit for evaluating MRI signals. The MRI unit has a high frequency antenna as well as a gradient coil system, the high frequency antenna device being arranged nearer to the examination space than the gradient coil system, as well as a high frequency shield arranged between the gradient coil system and the high frequency antenna device. The PET unit part is arranged between the high frequency shield and the high frequency antenna device. A shielding cover for the high frequency antenna device faces the high frequency antenna device. The shielding cover is opaque to high frequency radiation.