The hyperpolarizabilities of three p-quinodimethane derivatives with low diradical character have been evaluated. As electron correlation effects rule the electric field response properties, wave function and density functional theory-based methods have been compared to benchmark values calculated with the coupled cluster method including single and double excitations as well as perturbative estimate of the triples [CCSD(T)]. The basis set effects have been further assessed. This study shows that the determination of the second hyperpolarizability with the CCSD method provides results in closest agreement with the CCSD(T) reference values. The use of MP2 level of theory performs well for the closed-shell compound but not for open-shell ones. Spin-projection UMP3 and UMP4 methods reproduce well UCCSD(T) values for the p-quinodimethane but not for the charged compound. Without spin projection correction, density functional theory with a large range of exchange-correlation functionals does not perform well for these systems. Similar effects have been observed for the polarizability and first hyperpolarizability, although these effects are smaller.