We have recorded the Fourier-transform infrared (FTIR) spectrum of the nu(3) fundamental band of WF6 in a continuous supersonic jet expansion with an instrumental bandwidth of 0.0024 cm(-1) (FWHM, full width at half maximum, unapodized), using a Bomem DA.002 spectrometer. Some parts of this band have also been recorded with 0.0007 cm(-1) bandwidth using a diode laser spectrometer combined with a pulsed slit jet expansion. A multiple-pass arrangement has been used for the slit jet to observe low-intensity lines. In each case, we have used a WF6:He mixture with a seeding ratio 1:3 leading to a rotational temperature of ca. 50 K. This work extends the previous investigation of Takami and Kuze [J. Chem. Phys. 80, 5994 (1984)] to much higher J transitions. In both P and R branches, rotational lines have been recorded for J up to 46-48. We have used a tensorial Hamiltonian adapted to the group chain O(3)superset ofO(h) and developed to the third order for the analysis of the spectra. A least-squares fit for each of the four main isotopic species: (WF6)-W-182, (WF6)-W-183, (WF6)-W-184, and (WF6)-W-186 results in band centers (in this order) 714.538 19, 714.214 06, 713.895 44, and 713.266 21 cm(-1). We report furthermore first results on the high-resolution spectra of nu(3) of ReF6, which exhibits a fourfold degenerate electronic ground state of G(g)' species in the O-h(S) group. Supersonic jet-FTIR spectra show a moderately structured relatively broad band, whereas the diode laser spectroscopy of the seeded jet in the range 708-733 cm(-1) results in line resolved spectra of high complexity. A preliminary analysis is discussed, while a complete analysis still represents an appreciable challenge.