The Kramers-Kronig transform of the purely absorptive real part Re (&) of the nondiagonal component of the complex dielectric tensor is applied for the first time to assign quantitatively the contributions from various individual interband transitions ( 5 4.6 eV) to the dispersive interband Faraday rotation (IFR) in Si and Ge. The data of Re (&) needed are determined from measurements of Faraday ellipticity and complex Kerr effect, respectively. I n particular, the following problems could be clarified: (i) the origin of the nonresonant change in sign of the rotation in Ge which is due to the competition mainly between negative contributions from E,, E, + A,, and Eh