The orbital-symmetry rules for superexchange couplings of unpaired electrons via ligands were applied to one-dimensional (1D) polymers composed of heteropoly transition-metal tetrathiolates (poly(M1TM2), T : tetrathiolate). The polymers composed of the Cu(II)-Fe(III)(LS) and Ni(II)(HS)-Fe(III)(LS) units are predicted to be ferromagnetic within 1D chains, whereas several polymers such as the Co(II)(HS)-Cu(II) alternating one are considered to be ferrimagnetic. Ferromagnetic metals, dense Kondo and spin-mediated superconductors composed of trinuclear M2TM1TM2 complexes (M1=Ni) are also designed on the basis of the theoretical results. According to these guiding principles, we have performed the synthesis of ferro- and ferrimagnetic polymers composed of heteropoly transition-metal tetrathiolates (poly(M1TM2), T : tetrathiolate). The magnetic measurements of the solids were also carried out and the observed intrachain effective exchange integrals are summarized.