Using the band theory, the nature of the spin exchange interaction between the unpaired electrons within the half-filled band of 1-D organic radical crystals, consisting of galvinoxyl radicals, is investigated theoretically. The various contributions to the Heisenberg effective exchange integral, J(eff), the direct, kinetic, and indirect. spin exchange, are evaluated quantitatively for the experimentally determined crystal structure. To establish the dependence of J(eff) on the crystal topology and geometry, the calculations are carried out for several artificial model 1-D crystals of the galvinoxyl radical and of the parent hydrocarbon radical. J(eff) was also calculated for different interplanar distances of the stacking in the real crystal.