We report a computational study on the chemical bonding of phosphonates and carboxylates to aluminum oxide surfaces and how the binding properties are related to the amount of water in the experimental environment. Two different surface structures were used in the calculations in order to model representative adsorption sites for the phosphonates and carboxylates and to account for the amorphous nature of the hydroxylated AlOx films in experiment. For the phosphonates, we find that the thermodynamically preferred binding mode changes between mono-, bi-, and tridentate depending on the surface structure and the amount of residual water. For the carboxylates, on the other hand, monodentate adsorption is always lower in energy at all experimental conditions. Phosphonates are more strongly bound to aluminum oxide than carboxylates, so that carboxylates can be replaced easily by phosphonates. The theoretical findings are consistent with those obtained in adsorption, desorption, and exchange reactions of n-alkyl phosphonic and carboxylic acids on AlOx surfaces. The results provide an atomistic understanding of the adsorption and help to optimize experimental conditions for self-assembly of organic films on aluminum oxide surfaces.