Wave mixing in a four-level system with coherent three-frequency excit
ation formed by two strong and one weak fields is considered. It was a
ssumed that a strong monochromatic field at a frequency omega(e) popul
ates excited electronic states, and waves with frequencies omega(1) (s
trong) and omega(2) (weak) create a biharmonic perturbation in a band
of fluorescent transitions of an excited system. Components of the non
linear polarization p(NL) at frequencies omega(3) = 2 omega(1) - omega
(2) and omega(4) = omega(e) + omega(1) - omega(2) are calculated for t
he steady-state case in all orders in the field strengths of omega(e)
and omega(1) and in the first order in the amplitudes of all the remai
ning waves. It is shown that a feedback at the frequency omega(d) = om
ega(1) - omega(2) affecting oscillating populations of levels appears
in strong pumping field (omega(e)). The differences in dependences of
p(NL)(omega(3)) and p(NL)(omega(4)) on the frequency detuning wd and t
he intensity of external fields are determined. The possibilities for
using saturation of resonant wave mixing for studying photodynamics of
multilevel systems are discussed.