One of the common features of bacterial genomes is a strong compositional asymmetry between differently replicating DNA strands (leading and lagging). The main cause of the observed bias is the mutational pressure associated with replication. This suggests that genes translocated between differently replicating DNA strands are subjected to a higher mutational pressure, which may influence their composition and divergence rate. Analyses of groups of completely sequenced bacterial genomes have revealed that the highest divergence rate is observed for the DNA sequences that in closely related genomes are located on different DNA strands in respect to their role in replication. Paradoxically, for this group of sequences the absolute values of divergence rate are higher for closely related species than for more diverged ones. Since this effect concerns only the specific group of orthologs, there must be a specific mechanism introducing bias into the structure of chromosome by enriching the set of homologs in trans position in newly diverged species in relatively highly diverged sequences. These highly diverged sequences may be of varied nature: (1) paralogs or other fast-evolving genes under weak selection; or (2) pseudogenes that will probably be eliminated from the genome during further evolution; or (3) genes whose history after divergence is longer than the history of the genomes in which they are found. The use of these highly diverged sequences for phylogenetic analyses may influence the topology and branch length of phylogenetic trees. The changing mutational pressure may contribute to arising of genes with new functions as well.