The electrical properties (dipole moment, polarizability, and first hyperpolarizabilities) of anhydride derivatives are studied using theoretical chemistry methods. Several DFT XC functionals have been used while reliable atomic basis sets have been selected for their evaluations. The variations of (hyper)polarizabilities as a function of the anhydride structure are consistent among the different functionals, which facilitates the deduction of structure–property relationships. It has been observed that (1) The dipole moment of maleic anhydride (2) increases when adding a methyl group (3) and even more when fusing a phenyl ring to get phthalic anhydride (1), in good agreement with experiment. (2) The average polarizability is mostly driven by the molecular size while the polarizability anisotropy presents more subtle variations as a function of the compound. (3) For 1 and 2, the calculated polarizability tensor components are in close agreement with the experimental data. (4) To a good extend, the HRS first hyperpolarizabilities follow the same ordering as the polarizability anisotropy. (5) The EFISHG first hyperpolarizabilities exhibit a completely different ordering while its sign depends on the orientation of the CO double bonds. Finally, since the first hyperpolarizability values of these anhydride derivatives are of moderate amplitude, like those of amino acids, several design strategies have been discussed for achieving their enhancement.