The nature and magnitude of the spin exchange interaction within the half-filled band of 1-D stacks of mixed radical ion crystals (MRIC) consisting of two hydrocarbons H-1 and H-2 with different ionization potentials and electron affinities have been investigated theoretically. In a fully reduced or oxidized I-D crystal, each elementary unit is an anion radical or a cation radical: (H-1... H-2)(.-) - - or - - (H-1... H-2)(.+) --. In contrast to organic radical cation (anion) crystals which consist of identical polycyclic hydrocarbons -(H-delta. . .H-delta)(.+)- or -(H-delta. . .H-delta)(.-)- with a metalic or semiconducting ground state, the ground state of some classes of MRICs is a magnetic one. The band theory of magnetic interaction in many electron or-systems is applied to calculate the different contributions of the effective Heisenberg exchange integral.