  We present theoretical results for superradiance, i.e. the collective
coherent decay of a radiating system, in a semiconductor heterostructure under
a strong quantizing magnetic field. We predict a strong peak (`Dicke-peak') in
the emission intensity as a function of time, which should be observable after
a short initial excitation of electrons into the conduction band. This peak has
a characteristic dependence on the magnetic field and should be observable on
sub-picosecond time scales. Furthermore, pumping of electrons and holes into
the systems at a rate T leads to a novel kind of oscillations with frequency
$\sim \sqrt{T}$ in the limit of the lowest Landau level.
