Calculations at MP2/6-31G(d) level predict a very large first hyperpolarizability (beta) for two phosphorus-containing oligomers, namely, polyphosphaacetylene, -(P=CH)(n)(-) and polyphosphasilyne, -(P=SiH)(n)(-), i.e., 212777 and 90811 a.u., respectively, at n = 16. These values are 5.3 and 2.3 times of that for the nitrogen analogue of polyphosphaacetylene, that is, polymethineimine. In striking contrast, polyborophosphene, -(PH=BH)(n)(-), is predicted to have extremely small beta values, with a beta/n value approaching zero at large n. The causes for the relative beta values in these four series are discussed, in light of the bonding structure, the pi bond strength, the size of the nuclei, and the degree of delocalization.