A process is provided for improving the stability of a hydrocarbon mineral oil, particularly a hydrocracked stock, normally susceptible to thermal oxidation and the effects of light rays and for decreasing the tendency of the oil to form sludge material. The process involves reacting the hydrocarbon mineral oil before or after conventional treatment, such as dewaxing operations, with a stabilizing agent, such as an olefin, alcohol, ester or alkyl halide in the presence of a heterogeneous acidic catalyst which includes acid resins, clays and aluminosilicates, and which has a controlled alkylation activity. The final oil product has improved light stability over a conventionally treated oil.