Quantum chemical DFT calculations using the B3LYP functionals have been carried out for the electronically unsaturated 16 VE five-coordinate osmium boryl-complexes [(PH3)(2)(CO)ClOs-BR2] and the 18 VE six-coordinate complexes [(PH3)(2)(CO)(2)ClOs-BR2] with BR2 = BH2, BF2, B(OH)(2), B(OHC=CHO), and Beat (cat = catecholate O2C6H4). The bonding situation of the Os-BR2 bond was analyzed with the help of the NBO partitioning scheme. The Os-B bond dissociation energies of the 16 VE complexes are very high, and they do not change very much for the different boryl ligands. The 18 VE complexes have only slightly lower bond energies than the 16 VE species. The Os-B bond in both classes of compounds is provided by a covalent sigma -bond which is polarized toward osmium and by strong charge attraction. Os-->B pi -donation is not important for the Os-B binding interactions, except for the Os-BH2 complexes. The stability of the boryl complexes [Os]-BR2 comes mainly from B<--R -donation. which is clearly higher than the Os-->B ct-donation. The intraligand charge distribution of the BR2 group changes little when the Os-B bond is formed, except for BH2. The CO ligand in [(PH3)(2)(CO)(2)ClOs-BR2] which is trans to BR2 has a relatively weak bond to the osmium atom.