  The nongeneric six- and eightdimensional orbits of SO(4,2) are described in
explicitly covariant way. The relevant Hamiltonian dynamical systems are
constructed and canonically quantized. It is shown that the resulting unitary
representations of conformal group fit into the classification described by
Mack (G. Mack, Comm. Math. Phys. 55 (1977),1).
