We have investigated spin and orbital magnetic moments of the Re 5d ion in the double perovskites A2FeReO6 (A = Ba, Sr, Ca) by x-ray magnetic circular dichroism (XMCD) at the Re L2,3 edges. In these ferrimagnetic compounds, an unusually large negative spin and positive orbital magnetic moment at the Re atoms was detected. The presence of a finite spin magnetic moment in a 'non-magnetic' double perovskite as observed in the double perovskite Sr2ScReO6 proves that Re has also a small, but finite intrinsic magnetic moment. We further show for the examples of Ba and Ca that the usually neglected alkaline earth ions undoubtedly also contribute to the magnetism in the ferrimagnetic double perovskites. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.