  Low-temperature quantum oscillations of the dHvA amplitude are shown to
persist far below the upper critical field of a strongly type-II
superconductor, due to the gapless nature of the BCS quasiparticle spectrum in
high fields. The dHvA amplitude in the superconducting state is smaller than
its normal state countpart by factor ~[max(T,Gamma]/delta]**2, where Gamma is
the damping. This factor reflects the presence of a small gapless portion of
the fermi surface, surrounded by regions where the BCS gap is large. The
agreement with recent experimental data on V3Si is very good.
