Structures, vibrational frequencies, atomization energies at 0 K, and heats of formation at 298 K were obtained for four oxyfluoride molecules, several of which are known to present difficulties for single reference ab initio methods. Whereas much of this work was carried out with coupled cluster theory, multireference configuration interaction calculations were also performed, as an independent check on the reliability of the former. The use of large basis sets (up through augmented sextuple zeta quality in some cases) and a simple basis set extrapolation formula enabled us to accurately estimate the complete basis set limit. However, to achieve near chemical accuracy (+/-1 kcal/mol) in the thermodynamic properties, it was necessary to include three corrections to the frozen core atomization energies, in addition to the zero-point vibrational energy: (1) a core/valence correction; (2) a Douglas-Kroll-Hess scalar relativistic correction; and (3) a first-order atomic spin-orbit correction. Several approaches to approximating the remaining correlation energy were examined. Theory and experiment are in good agreement for the structures, with the largest difference associated with the FO bond length of FOOF, where the best theoretical value is 0.020 Angstrom shorter than experiment. Agreement with the available experimental heats of formation is good for FO and FO and much worse for FOO and FOOF. The final theoretical heats of formation (kcal/mol) at 298 K are 27.9 +/- 0.4 (FO), 6.6 +/- 0.5 (F2O), 9.6 +/- 0.6 (FOA and 9.6 +/- 0.9 (FOOF), where the uncertainties include an estimate for the intrinsic errors in the calculations. The corresponding experimental values adopted by the NIST-JANAF tables are 26.1 +/- 2.4 (FO), 5.9 +/- 0.5 (F2O), 6.1 +/- 0.5 (FO2), and 4.6 +/- 0.5 (FOOF). We suggest that the values reported here for FO and FO2 are the most reliable values available for these species and recommend their use. For FOOF, the current theoretical as well as that of others differ significantly from experiment and we recommend their use. Our theoretical value for FOOF has the smallest estimated error limits. In light of the demonstrated accuracy of the approach followed here for a large number of molecules and the magnitude of the discrepancy between theory and experiment for FO2 and FOOF, a reexamination of these systems by experimentalists appears justified.