Over recent years, evidence has been accumulating in favour of the free radical theory of aging, first proposed by Harman. Despite this, an understanding of the mechanism by which cells might succumb to the effects of free radicals has proved elusive. This paper proposes such a mechanism, based on a previously unexplored hypothesis for the proliferation of mutant mitochondrial DNA: that mitochondria with reduced respiratory function, due to a mutation or deletion affecting the respiratory chain, suffer less frequent lysosomal degradation, because they inflict free radical damage more slowly on their own membranes. Once such a mutation occurs in a mitochondrion of a non-dividing cell, therefore, mitochondria carrying it will rapidly populate that cell, thereby destroying the cell's respiratory capability. The accumulation of cells that have undergone this transition results in aging at the organismal level. The consistency of the hypothesis with known facts is discussed, and technically feasible tests are suggested, of both the proposed mechanism and its overall contribution to mammalian aging.