The theory of two-phonon resonant Raman scattering with the participat
ion of the quasi-two-dimensional (Q2D) excitons as intermediate states
is developed for a quantum well (QW). It is shown that the excitonic
channel of 2PRRS leads to the sharp enhancement ( in alpha0-3/ln2 alph
a0 times, alpha0 is the dimensionless exciton-LO-phonon coupling const
ant ) of the 2PRRS cross section in a comparison with the similar proc
ess in a bulk semiconductor. This enhancement is due to the possibilit
y of the real LO-phonon emission in the excitonic channel.