The present invention relates to chemical compounds, to pharmaceutical and veterinary compositions, and to the use of such compositions for the treatment or prevention of neurodegenerative pathologies and syndromes such as Parkinson's disease, Alzheimer's disease, lesions due to ischaemia and reperfusion, traumatic brain lesions, neuropathy due to HIV, Down's syndrome, diabetic polyneuropathy, muscular dystrophy, multiple sclerosis, Huntington's disease, prion disease, late dyskinesia, tauopathy and demyelinating pathologies, and other life-threatening pathologies such as cardiac/renal/pulmonary/hepatic/intestinal ischaemia-reperfusion, hypertension, diabetes, cancer, shock, toxicity due to drugs and radiation (radiotherapy and radiation protection), inflammatory conditions, atherosclerosis, aging, hyperlipidaemia, hypercholesterolaemia, epilepsy, and rheumatoid arthritis, all of which are known to be associated with an excess production of reactive free radicals. More particularly, the present invention relates to compositions containing antioxidant cyclic (bis)-hydroxylamines derived from N-piperidine as pharmaceutical compositions for the prevention and treatment of pathologies in man and in animals.