  The semi-classical Lifshitz-Kosevich (LK) description of quantum oscillations
is extended to a multiband two-dimensional Fermi liquid with a constant number
of electrons. The amplitudes of novel oscillations with combination
frequencies, recently predicted and observed experimentally, are analytically
derived and compared with the single-band amplitudes. The combination
amplitudes decay with temperature exponentially faster than the standard
harmonics, and this provides a valuable tool for their experimental
identification.
