  The unusual two-photon emission by Bose-condensed excitons caused by
simultaneous recombination of two excitons with opposite momenta leaving the
occupation numbers of excitonic states with momenta $p nonequal to 0$ unchanged
(below coherent two-exciton recombination) is investigated. Raman scattering
accompanied by the analogous two-exciton recombination (or creation) is also
analyzed. The excess momentum equal to the change of the electromagnetic field
momentum in these processes can be transferred to phonons or impurities. The
processes under consideration take place if there is Bose condensation in the
interacting exciton system, and, therefore, can be used as a new method to
reveal exciton Bose condensation. If the frequency of the incident light
$\omega< 2\Omega$ ($\Omega$ is the frequency corresponding to the recombination
of an exciton with p=0), the coherent two-exciton recombination with the excess
momentum elastically transferred to impurities leads to the appearance of the
spectral line $2\Omega-\omega$ corresponding to the induced two-photon
emission. In this case the anti-Stokes line on frequency $\omega+2\Omega$ also
appears in the Raman spectrum. If $\omega>2\Omega$, there are both Stokes and
anti-Stokes lines on frequencies $\omega\pm2\Omega$ in the Raman spectrum. The
induced two-photon emission is impossible in this case. The spectral lines
mentioned above have phonon replicas on frequencies $|\omega\pm
(2\Omega-n\omega^s_0)|$ corresponding to the transmission of the excess
momentum (partially or as a whole) to optical phonons of frequency $\omega^s_0$
($n$ is an integer number).
