Static and dynamic second hyperpolarisabilities of the furan homologues C4H4X (X = O, S, Se, Te), were investigated at ab initio HF and DFT levels using the POL Sadlej basis sets. The results show a monotonic increase of the property along the series with (C4H4X) essentially determined by (X), whereas dispersion contributions are almost constant. By comparison with CCSD(T) results, electron correlation contributions are well computed by the B3LYP method. Experimental values are reproduced within ca. 30% except for tellurophene, where it is underestimated by 85%.