Density functional calculations are used to generate a series of the maximum-spin lithium clusters Li-n+1(n) (n=2-12). These clusters do not possess any electron pairs and have formally a bond order of zero but are nevertheless strongly bound by what we describe here as "ferromagnetic bonding" (FM bonding). The FM bonding energy rises from 1.7 kcal mol(-1) for the dimer to 145 kcal mol(-1) for the dodecamer, and the bond energy per atom converges for cluster sizes of n = 11-12 reaching values of 11-12 kcal mol(-1) atom(-1). In line with previous studies of such clusters (Isr. J. Chem. 1993, 33, 455; J. Phys. Chem. A 2000, 104, 11223), FM bonding is found to prefer highly symmetrical egg-shaped structures with a high coordination number for the Li atom. The mechanism of FM bonding is elucidated using, a valence bond (VB) model equation and an orbital picture, which are projected from previous detailed calculations of the Li-3(2) dimer (J. Am. Chem. Soc. 1999, 121, 3165). The VB model is shown to capture the essence of FM bonding. Thus, the shape of the cluster, its steeply rising bond energy, and the convergence of the bonding energy per single atom all find a simple rationale in the VB model. It turns out that FM bonding is a delocalized covalent-ionic fluctuation that spreads over the entire cluster. This unique bonding type is likely to manifest also in clusters of noble elements. The strong bonding and high-spin state suggest that such clusters should have a long enough lifetime to be observed.