Directional mutation pressure associated with replication processes is the main cause of the asymmetry between the leading and lagging DNA strands in bacterial genomes. On the other hand, the asymmetry between sense and antisense strands of protein coding sequences is a result of both mutation and selection pressures. Thus, there are two different ways of superposition of the sense strand, on the leading or lagging strand. Besides many other implications of these two possible situations, one seems to be very important - because of the asymmetric replication-associated mutation pressure, the mutation rate of genes depends on their location. Using Monte Carlo methods, we have simulated, under experimentally determined directional mutation pressure, the divergence rate and the elimination rate of genes depending on their location in respect to the leading/lagging DNA strands in the asymmetric prokaryotic genome. We have found that the best survival strategy for the majority of genes is to sometimes switch between DNA strands. Paradoxically, this strategy results in higher substitution rates but remains in agreement with observations in bacterial genomes that such inversions are very frequent and divergence rate between homologs lying on different DNA strands is very high.