CoMo catalysts were prepared using Al2O3-MgO-(X) hybrid supports, where X = K2O or Li2O. The textural, structural and acid-base properties of these materials were characterized by several techniques. The catalysts were preliminarily evaluated in the hydrodesulfurization (HDS), hydrogenation (HYD) and hydrocracking (HCK) model reactions. The aims of this work are to identify the effect of the addition of an alkaline oxide (either K2O or Li2O) to the Lewis acid sites in the CoMo/Al2O3-MgO formulation; and on the other hand, to establish a relationship between the acidity and the catalytic performance (hydrogenation function). The results obtained from the pyridine thermodesorption analysis and the n-butyl amine titration techniques show that the incorporation of an alkaline oxide to the CoMo/Al2O3-MgO formulation causes a slight decrease in the total number of acid sites (TNAS) with respect to Al2O3 and the Al2O3-MgO hybrid supports. Both the enhanced textural and structural stability of the CoMo/Al2O3-MgO-(X) catalytic formulations, which could be probably attributed to the incorporation of Li or K cations to the MgO framework, stabilizing it, can also be observed. As for the catalytic performance, the CoMo/Al2O3-MgO-(X) catalysts containing either Li2O or K2O, show a decrease in both the HYD and HYC conversions; however, the formulation containing Li2O shows the best catalytic behavior due to both the low n-octane yield and the low hydrocracking activity.