Fourier transform infrared spectra of KrF2, XeF2, and monoisotopic (XeF2)-Xe-136 have been recorded in the nu(3), and nu(1)+nu(3) ranges with an effective resolution of 0.003-0.007 cm(-1). About 10 000 rovibrational lines belonging to cold bands and to hot bands with nu(1), nu(2), 2 nu(2), and nu(3) as lower levels have been assigned and fitted. The high-resolution results from this work and from two previous studies provide a rather complete set of precise spectroscopic constants and accurate ground-state and equilibrium geometries for both molecules. In the case of (KrF2)-Kr-84, r(0)=188.2821(9) pm supersedes previous incorrect r(0) values, and r(e)=187.6930(23) pm represents the first determination of the Kr-F equilibrium distance. Ab initio calculations employing effective core potentials and polarized double-zeta basis sets have been carried out at the following levels : self-consistent-field (SCF) theory, the Moller-Plesset second order perturbation theory (MP2), and coupled cluster theory with single and double excitations (CCSD) and a perturbational treatment of triple excitations (CCSD(T)). Pronounced correlation effects are found, especially for KrF2. The agreement between the correlated theoretical and the experimental results is generally quite good. A theoretical analysis clarifies the origin of the positive alpha(2) vibration-rotation coupling constants which have been observed for the bending vibrations in both molecules. Reliable harmonic and anharmonic force fields are presented for KrF2 and XeF2.