The global reaction between acetic anhydride and a fatty acid yields, at equilibrium, an asymmetric acetic-aliphatic anhydride in a medium containing finally: acetic-fatty anhydride, acetic anhydride, fatty acid, acetic acid and fatty anhydride. No solvent or catalyst was used to evaluate the impact of the actual reactivity of the anhydrides. The competition between the formation of acetyl and fatty acyl ester functions was evaluated by determining the ratio of acetyl/fatty acyl groups grafted on solid cellulose. The influence of temperature, reaction time, and length of fatty chain on the total degree of substitution and on the ratio of acetyl/fatty acyl ester functions was investigated. For the first time, a correlation has been established between esterification and the length of the aliphatic chain of the fatty acid. Reactivity of the medium decreased with the number of carbons in the fatty acid, raised to the power 2.37.