Relativistic supermultiplet schemes based upon broken inhomogeneous group (IHG) and broken noncompact group (NCG) symmetries are reviewed. The influence of symmetry breaking on matrix elements, via the spectrum of intermediate states in unitarity, is more violent in NCG than in IHG theories. In the exact-symmetry limit, NCG theories predict zero magnetic moments, while IHG theories say nothing without the additional assumption of vector meson dominance. The space components of axial currents may be successfully connected with generators of NCG symmetries, but for one fact—the known time-component commutators are not then included in the theory. To do this requires a larger group, such asSL12. Disadvantages of this group are overcome if all particles have zero mass in the exact-symmetry limit. The effective classification group is then anSU6, and the usualSU6w results remain. AlthoughSL12 contains the chiral groupSU3×SU3, the less satisfactory features of this group are removed by a re-allocation of particle states among its representations. For energies and momentum transfers large compared with the masses, a new groupSU6C is expected to hold forcoplanar processes. As a consequence, the results ofSU6w for forward and backward scattering differential cross-sections are predicted to hold for general scattering angles provided thats, |t|, |u|≫m2.