Rotational spectra of KrCuF and KrCuCl have been measured in the frequency range 8-18 GHz, using a pulsed jet cavity Fourier transform microwave spectrometer. The molecules were prepared by ablating Cu metal with a pulsed Nd:YAG laser (1064 nm) and allowing the plasma to react with appropriate precursors (Kr plus SF6 or Cl-2) contained in the backing gas of the jet (Ar or Kr). Rotational constants, internuclear distances, vibration frequencies, and 83 Kr, Cu, and Cl nuclear quadrupole coupling constants have all been evaluated, The Kr-Cu bonds are short and the complexes are rigid. The Kr-83 coupling constant of KrCuF is large (128.8 MHz). The Cu nuclear quadrupole coupling constants differ radically from those of uncomplexed CuF and CuCl molecules. The results are supported by those of ab initio calculations, which have also yielded Mulliken populations, MOLDEN plots of valence molecular orbitals and Laplace concentrations, and electron localization functions. The results are consistent with those reported earlier for other noble gas-noble metal halide complexes. The results have been used to assess the nature of the bonding in the complexes and have produced good evidence for weak noble gas-noble metal chemical bonding.