We present magneto-optical ( MO) Faraday spectra measured at the 3(p) edges of Fe, Co, and Ni. A polarization analysis of the final state of the transmitted radiation is employed to determine the Faraday rotation at these edges. The MO effect becomes resonantly enhanced at the 3p edges and accordingly large values for the intrinsic rotation constant k of 2.2 x 10(5), 1.5 x 10(5) and 0.8 x 10(5) deg/mm for the three ferromagnetic elements Fe, Co, and Ni, respectively, have been measured. These values are large and comparable to those observed at the 2p edges. This remarkable feature emphasizes the importance of the exchange ( EX) splitting over the spin-orbit ( SO) interaction of the core levels in determining MO effects in the extreme ultra-violet ( EUV) region. From these measurements the complete set of MO constants at the 3p edges has been derived.