An ab initio study on the I:2 and 1:2 van der Waals complexes between boron trifluoride and carbon monoxide has been carried out. Full geometry optimizations are performed at the MP2/6-31G* and MP2/D95* levels. The bond energies computed at different levels (MP2, MP4) and with several basis sets (6-31G*, D95*, and aug-cc-pVDZ) range from 3.2 to 3.5 kcal/mol for BF...CO and from 6.4 to 6.6 kcal/mol for OC...BF3...CO. The counterpoise-corrected values range from 0.7 to 1.6 kcal/mol for BF3...CO and from 1.3 to 3.1 kcal/mol for OC...BS3...CO. These (gas phase) computed values are consistent with the corresponding experimental dissociation enthalpies as measured in liquefied argon (1.8 and 3.5 kcal/mol). The MP2/6-31G* computed vibrational frequencies agree quite well with the infrared measurements. The analysis of The frequencies together with the energetic data gives theoretical support to some tentative assignments proposed in the infrared studies, The experimental suggestion about the formation of the never observed before BF3...OC and OC...BF3...CO adducts is theoretically confirmed. A theoretical analysis of the wave functions shows that the weakness oi the complexes formed can be ascribed to the small charge transfer detected.