Background. The ability to form a cellular memory and use it for cellular decision-making could help bacteria to cope with recurrent stress conditions. We analyzed whether bacteria would form a cellular memory specifically if past events are predictive of future conditions. We worked with the asymmetrically dividing bacterium Caulobacter crescentus where past events are expected to only be informative for one of the two cells emerging from division, the sessile cell that remains in the same microenvironment and does not migrate. Results. Time-resolved analysis of individual cells revealed that past exposure to low levels of antibiotics increases tolerance to future exposure for the sessile but not for the motile cell. Using computer simulations, we found that such an asymmetry in cellular memory could be an evolutionary response to situations where the two cells emerging from division will experience different future conditions. Conclusions. Our results raise the question whether bacteria can evolve the ability to form and use cellular memory conditionally in situations where it is beneficial.