  We consider two well-known classes of unitarization of Born amplitudes of
hadron elastic scattering. The standard class, which saturates at the black
disk limit includes the standard eikonal representation, while the other class,
which goes beyond the black-disk limit to reach the full unitarity circle,
includes the U matrix. It is shown that the basic properties of these schemes
are independent of the functional form used for the unitarisation, and that U
matrix and eikonal schemes can be extended to have similar properties. A common
form of unitarisation is proposed interpolating between both classes. The
correspondence with different nonlinear equations are also briefly examined.
