Occupational mismatch is a widespread phenomenon among immigrants in many European countries. Mismatch is predominantly measured in terms of formal education ignoring the imperfect comparability of international educational degrees. Exploiting internationally comparable cognitive skill measures from the PIAAC data, we examine whether overeducation implies only an apparent phenomenon or a genuine overqualification observed also in the form of cognitive overskilling. Our results for 11 European countries show significant differences in the incidence of formal overeducation and genuine overqualification between immigrants and natives.