The nature of the bonding in OCF3- and the isoelectronic molecule ONF3 has been the subject of much discussion for many years, because these species appear to have unusual bond lengths and angles. We have reinvestigated the nature of the bonding in these and some related molecules by analyzing their calculated electron density distributions. The results show that the bonding in the series OBF32-, OCF3-, ONF3 ranges from predominately ionic in OBF32- to predominately covalent in ONF3 and that the interligand distances are consistent with the close packing of the Ligands around the central atom. The AO bonds (A = B, C, N) are double bonds ranging in nature from a very ionic B=O bond to a predominately covalent N=O double bond, but all three are strong and short so that, in accordance with the ligand close packing (LCP) model, the AF bonds are correspondingly long. Also consistent with this model the bonds in a three-coordinated AOF(2) molecule are shorter than those in the corresponding AOF(3) molecule. Protonation of the doubly bonded oxygen, which converts the A=O bond to a single A-OH bond in each case, considerably lengthens the A-O bond, and the bond angles accordingly adopt values much closer to the tetrahedral angle. The difficulties of trying to describe the bonding in these molecules in terms of Lewis structures are discussed.