Compositions and methods for protecting neural tissue (e.g., neurons) from anoxia and spreading depression (SD) involve inhibiting the cGMP-dependent protein kinase (PKG) pathway. It was discovered that the PKG pathway plays a crucial role in regulating SD and tolerance to anoxia in the central nervous system (CNS). Inhibition of the PKG pathway greatly reduces SD and increases tolerance to anoxia (i.e., hypoxia), while activation of the pathway exacerbates SD pathology. The compositions and methods can be used to treat any condition associated with SD or anoxia, including stroke, spinal cord injury, neurogenerative disease, dizziness, headaches, and migraines.