There is evidence to suggest that eukaryotic genomes are subject to frequent insertions and deletions of non-coding DNA. This may lead to a gradual increase or decrease in genome size, or to a dynamic equilibrium in which the overall size remains constant. We argue, however, that there is a bias favouring an accumulation of non-coding DNA in the proximity of genes. Such bias causes a progressive change in genome structure regardless of whether the overall genome size increases, decreases or remains constant. We show that this change may serve as a 'molecular clock', supplementing that provided by nucleotide substitution rates.