We have studied the electronic structure of the ferromagnetic double perovskites Sr2CrReO6, Sr2CrWO6 and Ba2FeReO6 by means of a full-potential linear muffin-tin orbital density-functional method. Our scalar-relativistic calculations predict these compounds to be half-metallic with a total magnetic moment of 1, 2, and 3 νB respectively. However, when the spin-orbit coupling is included, the 5d transition Re and W ions exhibit substantial unquenched orbital magnetic moments, resulting in a significant increase of the total magnetic moment. The half-metallic gap turns into a pseudo-gap in Sr 2CrReO6 and Ba2FeReO6 when the spin-orbit coupling is included whereas Sr2CrWO6 remains half-metallic even with spin-orbit coupling. The calculated spin and orbital magnetic moments agrees well with the recent experimental XMCD measurements. © 2006 IOP Publishing Ltd.