  A general covariant quantization of superparticle, Green-Schwarz superstring
and a supermembrane with manifest supersymmetry and duality symmetry is
proposed. This quantization provides a natural quantum mechanical description
of curved BPS-type backgrounds related to the ultra-short supersymmetry
multiplets. Half-size commuting and anticommuting Killing spinors admitted by
such backgrounds in quantum theory become truncated $\kappa$-symmetry ghosts.
The symmetry of Killing spinors under dualities transfers to the symmetry of
the spectrum of states.
  GS superstring in the generalized semi-light-cone gauge can be quantized
consistently in the background of ten-dimensional supersymmetric gravitational
waves. Upon compactification they become supersymmetric electrically charged
black holes, either massive or massless. However, the generalized light-cone
gauge breaks S-duality. We propose a new family of gauges, which we call black
hole gauges. These gauges are suitable for quantization both in flat Minkowski
space and in the black hole background, and they are duality symmetric. As an
example, a manifestly S-duality symmetric black hole gauge is constructed in
terms of the axion-dilaton-electric-magnetic black hole hair. We also suggest
the U-duality covariant class of gauges for type II superstrings.
