A method for providing to a mammal a neuroprotective effect against a brain pathology that is associated with reactive oxygen species originating from mitochondria (mROS). The method includes the step of administering to the mammal an SkQ mitochondria-targeted antioxidant in an amount effective to provide said neuroprotective effect. The SkQ mitochondria-targeted antioxidant may be administered either prophylactically or for treatment with respect to brain pathologies other than brain trauma or stroke, and may be administered for treatment of brain trauma or stroke.