The intensity of two-photon-excited fluorescence measured relative to the intensity of hyper-Rayleigh scattering in the same apparatus was used to determine the two-photon-excited fluorescence cross sections of the xanthene dyes Rhodamine B, Rhodamine 6G, and Fluorescein. The measured cross sections at Xo = 1064 nm are sigma(2PF)((2)) = 1.5 +/- 0.3 X 10(-50) cm(4) s, 2.0 +/- 0.4 x 10(-50) cm(4) s, and 1.4 +/- 0.3 x 10(-524) cm(4) s, for the three dyes, respectively. The two-photon-excited fluorescence cross section of Rhodamine B was also calibrated with one-photon-excited fluorescence in this apparatus. The result, sigma(2PF)((2)) = 2.3 +/- 0.7 X 10(-50) cm4 s, is in reasonable agreement with the result calibrated by hyper-Rayleigh scattering. The results for Rhodamine B are 1.5-6 times smaller than previous results calibrated by one-photon-excited fluorescence. (C) 1999 Optical Society of America [S0740-3224(99)01406-X] OCIS codes: 190.4180, 190.4710, 300.2530, 300.6410.