Models for the behavior of the second hyperpolarizability of alternating linear chains of the type A-B-A-B-A-B-.... are presented. Systems of interest are studied using a two-band Hubbard Hamiltonian. Setting the Hamiltonian parameters to appropriate values, the models may be used to study substituted homonuclear chains, substituted or unsubstituted heteronuclear chains, or alternating metal-ligand polymers. Two types of chemical control are readily accessible: substitution and doping. One of the Hamiltonian parameters, the A-B energy gap, is chemically controllable by substitution. The total number of electrons is controllable by doping. The model predicts that the magnitude and sign of the second hyperpolarizability can be changed drastically in some of these systems by chemical substitution or doping. However, the effects of these two types of chemical modifications are highly dependent on electron correlation.