A comprehensive study was performed on the brains of various vertebrate species showing different life energy potentials in order to find out if free radicals are important determinants of species-specific maximum life span. Brain superoxide dismutase, catalase, Se-dependent and independent GSH-peroxidases, GSH-reductase, and ascorbic acid showed significant inverse correlations with maximum longevity, whereas GSH, uric acid, GSSG/GSH, in vitro peroxidation (thiobarbituric acid test), and malondialdehyde (measured by HPLC), did not correlate with maximum life span. Superoxide dismutase, catalase, GSH-peroxidase, GSH and ascorbate results agree with those previously reported in various independent works using different animal species. GSSG/GSH, and true malondialdehyde (HPLC) results are reported for the first time in relation to maximum longevity. The results suggest that longevous species simultaneously show low antioxidant concentrations and low levels of in vivo free radical production (a low free radical turnover) in their tissues. The "free radical production hypothesis of aging" is proposed: a decrease in oxygen radical production per unit of O2 consumption near critical DNA targets (mitochondria or nucleus) increases the maximum life span of extraordinarily long-lived species like birds, primates, and man. Free radical production near these DNA sites would be a main factor responsible for aging in all the species, in those following Pearl's (Rubner's) metabolic rule as well as in those not following it.