In anABA symmetric and linear trinuclear system where the interaction between terminal ions is assumed to be negligible, the distribution in energy of the spin states depends on the relative values of the spinsSA andSB. If 2SA≤SB, the spin state structure is regular in the sense where the spin multiplicity varies monotonically with the energy; if 2SA>SB; it is irregular. A Cu(II)Ni(II)Cu(II) triad illustrates the former situation and a Mn(II)Cu(II)Mn(II) the latter. The concept of irregular spin state structure may be extended to the ordered bimetallic chains (AB)N withN→∞. The main theoretical ideas concerning these systems are presented as well as some typical examples. In particular, it is shown that a Cu(II)Mn(II) chain with an antiferromagnetic interaction between nearest neighbors exhibits a ferromagnetic-like behavior in the low temperature range. This corresponds to one-dimensional ferrimagnetism. Finally, it is emphasized that this concept of irregular spin state structure might lead to the first genuine molecular ferromagnets.