Nondegenerate four-wave mixing (FWM) is considered in a medium in whic
h frequencies of one pair of interacting light waves are resonant with
the absorption band, while frequencies of two other waves ate resonan
t with the fluorescence band (two-resonance FWM). Based on calculation
s performed for homogeneous and inhomogeneous bands, it was concluded
that the nonlinear cubic susceptibility chi((3)) of a system is highly
sensitive to the relation between frequency detuning of the pumping w
aves and the energy relaxation rate. The possibilities of four-wave an
d three-wave mixing in studies of molecular photodynamics are compared
. It is shown that ultrafast relaxation between levels of the excited
or ground electronic states of molecules can be selectively studied by
combining resonance conditions upon four-wave mixing.