The atomic polarizabilities of carbon dioxide and xarbodiimide, HN═C═=NH, have been studied with ab initio theoretical methods. Structures were optimized and properties were determined using RHF, MP2, and QCISD theories and a variety of basis sets up to quadruple-ξ quality. The static electric dipole polarizability tensor components were determined using the finite field method. The isotropic polarizability 〈α〉 and the anisotropic polarizabilities Δα and κ were calculated for both heterocumulenes from the respective tensor components. The experimental tensor components and polarizabilities 〈α〉, Δα, and κ are known for carbon dioxide, and these values are used to assess the accuracy of the theoretical methods. This knowledge about the achievable accuracy is then employed in the prediction of the polarizability values of carbodiimide. The only measurable polarizability values for carbodiimide are 〈α〉 and κ. The best level of theory employed in this study is QCISD(fc)/6-311++G(3df,2pd) and this level gives 〈α〉 and κ values of 16.722 and 0.289 au3 for carbon dioxide. These values deviate somewhat from the experimental values of 17.762 and 0.267 au3 and we rationalize these differences based on the calculated polarizability tensor components. The calculated 〈α〉 and κ values of carbodiimide are 28.963 and 0.310 au3. Taking into account the deviations from experiment for the carbon dioxide values, we predict 〈α〉 and κ values of 30.764 and 0.286 au3 for carbodiimide. The discussion emphasizes the important role of the inclusion of three sets of d-polarization functions. The third, diffuse set of d-functions is essential to polarize the electron density described by the diffuse functions and also by the outer valence p-functions.