The nonlinear optic coefficients of ferroelectrics in the far-infrared reso
nance region can be determined by means of a systematic expansion based on
the Landau-Devonshire free-energy expansion together with the Landau-Khalat
nikov dynamical equations. The formalism is reviewed and the general struct
ure of the chi((2)) and chi((3)) coefficients is discussed. Examples of the
frequency and temperature dependence of selected coefficients are presente
d. We conclude with brief discussions of possibilities for experimental mea
surement of the nonlinear-optic coefficients and of possible applications.