An ab initio study is carried out to investigate the anionic aerogen bonds in complexes of KrO3, XeO3 and XeOF2 with F-, Cl-, Br-, CN-, NC-, N3-, SH-, SCN-, NCS-, OH- and OCH3- anions. All of the anionic aerogen bonds analyzed here have a partial covalent character. Charge transfer from the anion to the Kr-O or Xe-O σ* orbital stabilizes these complexes and leads to a sizable redshift in the corresponding stretching frequencies. The J(Kr-O) or J(Xe-O) spin-spin coupling constants can be regarded as a useful tool for the characterization of strength of the anionic aerogen-bonded complexes.