The present invention relates to chemical compounds, to pharmaceutical andveterinary compositions, and to the use of such compositions for the treatmentor prevention of neurodegenerative pathologies and syndromes, such asParkinson's disease, Alzheimer's disease, lesions due to ischaemia andreperfusion, traumatic brain lesions, neuropathy due to HIV, Down's syndrome,diabetic polyneuropathy, muscular dystrophy, multiple sclerosis, Huntington'sdisease, prion disease, late dyskinesia, tauopathy and demyelinatingpathologies, and other life-threatening pathologies such ascardiac/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, andrheumatoid arthritis, all of which are known to be associated with an excessproduction of reactive free radicals. More particularly, the present inventionrelates to compositions containing antioxidant cyclic (bis)-hydroxylaminesderived from N-piperidine as pharmaceutical compositions for the preventionand treatment of pathologies in man and in animals.