With the help of the Linearized Augmented Plane Wave (LAPW) method, the role of some structural types of CoTiSb alloy in the formation of its energy, spatial, spectral, and spin characteristics has been clarified. The ground state of CoTiSb alloy, which is characterized by the highest cohesive energy, is found to be realized in the case where atoms and vacancies are arranged like in the C1b phase. Transitions to the L2 and B2 phases with different arrangements of alloy components in their crystal lattices are accompanied by the emergence of high-energy metastable states. CoTiSb alloy in the ground state is a nonmagnetic insulator. The metastable phases transform into metals with spin-polarized electron states and magnetic moments mainly localized at cobalt atoms. K e y w o r d s: band structure calculations, X-ray electron spectra, spintronics.