MgAl2O4 and ZnAl2O4 spinels have been irradiated by swift heavy ions (Kr-86 and S-36) simulating the irradiation by fission products for applications in the transmutation targets. The structures of unirradiated and irradiated spinel samples have been studied by NMR spectroscopy, with Al-21 magic angle spinning and multiple-quantum magic angle spinning experiments. The parameters of fluence and electronic stopping power have been compared. For Kr-86 ions, the obtained spectra are modified by irradiation: we observe a rise of the amount of aluminum in tetrahedral sites and a widening of the lines associated with the different aluminum environments compared with those of the pristine samples. Site exchange in the cationic sublattice is then observed and can be quantified from NMR spectra, determining the inversion parameter. An inversion parameter of 0.77 is estimated for the MgAl2O4 spinel irradiated with 10(13) Kr ions/cm(2), for a value of 0.275 in the pristine samples. Moreover, a line attributed to aluminum in 5-fold coordination with oxygen is observed in irradiated spinel samples at the maximum fluence for krypton. These new aluminum environments can characterize a transition layer which could change toward an amorphous layer, increasing the electronic stopping power and/or the fluence.