Abstract The theoretical models of narrow-band high-spin systems and those experimentally investigated so far are mainly polyconjugated π-electron systems for which the presence of degenerate states follows from the molecular topology. The purpose of the present theoretical treatment is the study of new classe of narrow-band organic polymers in which the narrow band is at least partially defined by structural principles other than the molecular topology. The polymers treated represent one-dimensional systems and each elementary units has one singly occupied molecular orbital (MO). The presence of a narrow band of degenerate or nearly degenerate quantum states (MOs) is caused by steric hindrance, which reduces the overlap between the interacting singly occupied orbitals in the limiting case to zero (the orbitals of adjacent repeat units are orthogonal), i.e. the repeat units are not in conjugation with one another in a classical π-sense. The effective exchange integral, J, in the Heisenberg Hamiltonian is investigated as a function of overlap between adjacent πa− and πb−AOs. It is shown that the ferromagnetic alignment is favoured for small overlap between the adjacent singly occupied π-orbitals. Two model polymers are considered: — a polyacetylene in which the 2p-AOs participating in the conjugation are situated at an angle of θ>0. It is shown that for θ⩾80° the effective exchange integral J>0, i.e. the exchange coupling interaction is ferromagnetic; — a polymer (−R.−)n the e