Molecular or polymeric-based magnetic materials have been the subject of increasing interest in recent years. Organic magnetic structures have been theoretically predicted by Ovchinnikov. One of the most attractive features of these new materials is the possibility of combining mechanical, electrical and/or optical properties of organic materials with magnetic properties. In the present work, we study a class of one-dimensional chains with special topologies that could lead to magnetic order. Using the Hubbard model, we find that these materials should exhibit ferrimagnetic ordering at half-filled band, in agreement with a theorem by Lieb. Away from half filling these systems display a rich magnetic phase diagram.8501/03/1517611762Lieb, E.H., The Hubbard model: Some rigorous results and open problems (1993) Proc. Conf. "Advances in Dynamical Systems and Quantum Physics", , Capri, (World Scientific, in press)Lieb, E.H., (1989) Phys. Rev. Lett., 62, p. 1201Silvestre, J., Hoffmann, R., (1985) Inorg. Chem., 24, p. 4108(1993) Synth. Metals, 55-57Yoshisawa, K., Tanaka, K., Yamabe, T., Yamauchi, J., (1992) J. Chem. Phys., 96, p. 5516(1991) Synth. Metals, 41-43, p. 3297Korshak, Yu.V., Medvedeva, T.V., Ovchinnikov, A.A., Spector, V.N., (1987) Nature, 326, p. 370Torrance, J.B., Oostra, S., Nazal, A., (1987) Synth. Metals, 19, p. 809MacDiarmid, A.G., Chiang, J.C., Richter, A.F., Epstein, A.J., (1987) Synth. Metals, 18, p. 285Nishide, H., (1995) Adv. Mater., 7, p. 937Macêdo, A.M., Dos Santos, M.C., Coutinho M.D. Filho, Macêdo, C.A., (1995) Phys. Rev. Lett., 74, p. 1851