Co-Si multiphase metallic samples have been studied by two-detector Doppler broadening and positron lifetime spectroscopy techniques. The experimental results together with theoretical calculations of positron lifetimes and momentum distributions of the annihilating core electrons has let us to determine the positron annihilation characteristic in both phases of each Co-Si multiphase alloy studied. In Co38.2Si61.8 alloy, Si vacancies trap positrons in the CoSi2 phase, whereas no trapping is found in the CoSi phase of the same sample. In the Co22.5Si77.5 alloy positrons annihilate only from delocalized states.