  Recently, observations with the Hubble Space Telescope have revealed small
stellar discs embedded in the nuclei of a number of ellipticals and S0s. In
this paper we construct two-integral axisymmetric models for such systems. We
calculate the even part of the phase-space distribution function, and specify
the odd part by means of a simple parameterization. We investigate the
photometric as well as the kinematic signatures of nuclear discs, including
their velocity profiles (VPs), and study the influence of seeing convolution.
The rotation curve of a nuclear disc gives an excellent measure of the central
mass-to-light ratio whenever the VPs clearly reveal the narrow, rapidly
rotating component associated with the nuclear disc. Steep cusps and seeing
convolution both result in central VPs that are dominated by the bulge light,
and these VPs barely show the presence of the nuclear disc, impeding
measurements of the central rotation velocities of the disc stars. However, if
a massive BH is present, the disc component of the VP can be seen in the wing
of the bulge part, and measurements of its mean rotation provide a clear
signature of the presence of the BH. This signature is insensitive to the
uncertainties in the velocity anisotropy, which often lead to ambiguity in the
interpretation of a central rise in velocity dispersion as due to a central BH.
