A theoretical approach is applied for estimation of the nature (ferro- or antiferromagnetic) of the spin exchange interaction between the unpaired electrons within the half-filled band of 1-D organic radical crystals, consisting of weakly interacting alternant radicals. The various contributions to the Heisenberg effective exchange integral, J(eff) - direct, kinetic, and indirect spin exchange - are evaluated quantitatively for several model crystals in order to establish the nature and magnitude of the exchange coupling between the unpaired spins. General rules are formulated showing the dependence of J(eff) on the crystal topology and geometry.