There are numerous reports on the role of oxidative stress in the origin of some neurodegenerative (Alzheimer's and Parkinson's) diseases; however, the information concerning molecular mechanisms of the observed effects is rather contradictory. This paper summarizes the review of our own works in this field and new experimental observations on the antioxidant action of some hydrophobic plant compounds. We discuss our hypothesis on the role of misfolded proteins in the regulation of the chaperone system involved in the genesis of amyloid neurodegenerative (prion and Alzheimer's) diseases, briefly describe the role of modification of the glycolytic enzyme glyceraldehyde-3-phosphate dehydrogenase in the inhibition of glycolysis and induction of the apoptosis of nerve cells, and suggest possible ways of the use of hydrophobic plant antioxidants for the prevention of amyloid transformation of proteins and other neurodegenerative processes.