We have previously shown that computer simulations of processes that generate selectively advantageous changes together with random duplications and deletions give rise to genomes with many different genes embedded in a large amount of dispensable DNA sequence. We now explore the consequences of neutral changes on the evolution of genomes. We follow the consequences of sequence divergences that are neutral when they occur in dispensable sequences or extra copies of genes present in multigene families. We find that when divergence occurs at about the same frequency as duplication/deletion events, genomes carry repetitive sequences in proportion to their size. Inspection of the genomes as they evolved showed that multigene families were generated by relatively recent duplications of single genes and so would be expected to be highly homogeneous.