Exciton states in wide-gap materials CaF 2 and BaF 2 have been studied with the technique of two-photon spectroscopy using synchrotron radiation and laser. The two-photon excitation spectrum of CaF 2 , and that of BaF 2 as well, exhibited a clear peak on the high-energy side of the 1S exciton energy. The peaks are attributed to the 2 P states of the valence excitons. According to this assignment, the binding energies of the excitons have been determined to be 0.8 and 0.9 eV for CaF 2 and BaF 2 , respectively. The signal intensities were larger than that in the case of one-beam excitation by a factor of about 500, which is attributed to a resonant effect on two-photon absorption. ͓S0163-1829͑99͒52836-1͔ RAPID COMMUNICATIONS