  We theoretically analyze the influence of magnetic field on small-signal
absorption and gain in a superlattice. We predict a very large and tunable THz
gain due to nonlinear cyclotron oscillations in crossed electric and magnetic
fields. In contrast to Bloch gain, here the superlattice is in an electrically
stable state. We also find that THz Bloch gain can be significantly enhanced
with a perpendicular magnetic field. If the magnetic field is tilted with
respect to the superlattice axis, the usually unstable Bloch gain profile
becomes stable in the vicinity of Stark-cyclotron resonances.
