The existence of a class of (very) high-spin hydrocarbons is predicted on the basis of (a) new theorems for valence-bond models, (b) classical structure theory, (c) standard theorems for molecular orbital theory, (d) several small-system calculations with Hubbard and PPP Hamiltonians, and (e) a large-system cluster expansion calculation applied to the polyallyl high-spin candidates. Some properties, especially the magnetic ones, for these conjugated alternants are briefly discussed. 1982 American Institute of Physics.