Starting with the Liouville equation and with help of the combined pro
jection technique, we formulate the nonlinear susceptibility for many
electron systems subject to-oscillatory external fields. For the itera
tive projections, we introduce the primary, secondary, the tertiary pr
ojection operators and so on. The final form for the averaged dynamica
l quantity is given in the form of a power series in the external fiel
d.