The main concern in face-processing research is to understand the processes underlying the identification of faces. In the study reported here, we addressed this issue by examining whether local or global information supports face identification. We developed a new methodology called "iHybrid." This technique combines two famous identities in a gaze-contingent paradigm, which simultaneously provides local, foveated information from one face and global, complementary information from a second face. Behavioral face-identification performance and eye-tracking data showed that the visual system identified faces on the basis of either local or global information depending on the location of the observer's first fixation. In some cases, a given observer even identified the same face using local information on one trial and global information on another trial. A validation in natural viewing conditions confirmed our findings. These results clearly demonstrate that face identification is not rooted in a single, or even preferred, information-gathering strategy.