The second hyperpolarizability of p-quinodimethane derivatives has been calculated at different levels of approximation, based on the wavefunction or on the electron density, in combination with a large range of basis sets. The main conclusions are i) the CCSD method provides results in the closest agreement with the CCSD(T) reference values with CCSD/CCSD(T) ratios amounting to 0.85, 1.26, and 0.88 for compounds 1-3, respectively, ii) the MP2 level of approximation performs well for the closed-shell compound 3 but not for the open-shell systems 1 and 2, iii) for compound 1, the projected UMP3 and UMP4 methods enable to reproduce the unrestricted CCSD(T) value but not for the charged compound 2 where high-order electron correlation effects are needed to reproduce the sign of γ, and iv) without spin projection correction, density functional theory with a broad range of XC functionals does not perform well for these systems with low diradical character, in particular for the charged species. Similar effects have been observed for the lower order properties (polarizability and first hyperpolarizability), though the effects are smaller.