The valence electronic structure of the half-metallicdouble perovskite Sr2FeMoO6 forms from a strongly hybridizedband in the spin-down channel of Fe 3d and Mo 4d states thatprovides metallic conductivity and a gapped spin-up channel. Theground-state description has previously been explored in terms ofmany-body interactions where local and nonlocal interactionsproduce states with a combination of a charge-transferconfiguration and intersite charge fluctuations. Here, we providea qualitative understanding on nonlocal effects in Sr2FeMoO6using a combination of core-level X-ray spectroscopies, specificallyX-ray absorption, emission, and photoelectron spectroscopies. Ourspectroscopic data indicate intersite Fe 4p−O 2p−Mo 4dinteractions to be the origin of these nonlocalized transitions.Close to the Fermi level, this interaction is dominated by Mo 4d−O 2p character. When our data are compared against first- principles electronic structure calculations, we conclude that a full understanding of the nature of these states requires a spin-resolved description of the hybridization functions and that the nonlocal screening occurs predominantly through hybridization in the minority spin channel of the Mo 4d bands.