Materials with low band gaps, down to 0.5 eV, can be obtained from polymers containing squaraine or croconaine moieties. The properties of poly-aminosquaraine, a representative of this novel class of materials, and related compounds have been investigated by both semiempirical and ab initio quantum mechanical methods. Formally, poly-aminosquaraine is a donor/acceptor compound. The band gap in these compounds is usually determined by, the interaction between the highest occupied molecular orbital (HOMO) of the donor and the lowest unoccupied molecular orbital (LUMO) of the acceptor. If the interaction is weak a small band gap results, but it will also lead to an unfavorably small dispersion of the bands. In poly-aminosquaraine the levels around the gap are well described by a three-level model, involving two acceptor levels and one donor-level. Symmetry forbidden interactions allow for a small band gap and a significant dispersion at the same time. In principle, by choosing different donors and accepters, the band gap can be manipulated. This is illustrated by results on poly-aminocroconaine and poly-amino-(2-propenolate).