We report here the X-ray magnetic circular dichroism (XMCD) study at the Gd M(4,5)- and L(2,3)-edges of two linear magnetic chains involving Gd(III) cations bridged by nitronyl nitroxide radicals. This spectroscopy directly probes the magnetic moments of the 4f and 5d orbitals of the gadolinium ions. We compare macroscopic magnetic measurements and local XMCD signals. The M(4,5)-edges results are in agreement with the J values extracted from the fits of the SQUID magnetic measurements. The L(2,3)-edges signals show that the electronic density in the Gd 5d orbitals depends on the neighbors of the gadolinium cations. Nevertheless, the 5d orbitals do not seem to play any role in the superexchange pathway between radicals through the metal ion proposed to explain the particular magnetic exchange interactions between the radicals in these chains.