Novel peptides, whose individual components are L-amino acids or D-amino acids are used as active ingredients in medicaments for treating diseases in which the increased occurrence of free radicals plays a pathophysiological role, or for treating diseases involving acute hypoxia or ischaemia in an organ system of the body, in particular in the central nervous system, or for treating iron-storage diseases such as Hallervorden-Spatz syndrome, or for treating neurodegenerative diseases, in particular Alzheimer's disease, the Lewy body variant of Alzheimer's disease, Parkinson's disease, multi-system atrophy, Lewy body dementia or Huntington's chorea and all syndromes that are similar to the neurodegenerative diseases.