A series of cobalt spinel catalysts dispersed over various alumina supports (with varying alpha-, gamma-, delta-and theta-Al2O3 phase contents) were prepared and thoroughly characterized (XRF, XRD, mu RS, SEM/TEM/EDX/SAED, TPR) and their reactivity was evaluated in low temperature N2O decomposition as a probe reaction. The observed significant differences in catalytic activities were discussed in terms of the support's nature, active phase dispersion, nanocrystal morphology and the alumina support-Co3O4 interactions. The more reactive amorphous phase as well as the gamma-, delta-and theta-Al2O3 phases gives rise to high dispersion of the spinel nanocrystals (similar to 10 nm) which is, however, sacrificed by the formation of mixed Co3-xAlxO4 spinels of much less activity. It was revealed that the best support for the deN(2)O catalyst is an alpha-Al2O3 phase of micrometric grain size and the optimal size of the Co3O4 nanocrystals is in the range of 20-30 nm. This catalyst was also found to be more resistant to H2O, NO and O-2 contaminants in comparison to the catalysts based on gamma-Al2O3.