A stochastic model was designed to describe the evolution of bacterial cultures during 10,000 generations. It is based on a decreasing law for the generation of beneficial mutations as they become fixed in the genomes. Seven beneficial mutations on average were necessary to improve the relative fitness from 1.0 to 1.43 and the model was consistent with the population biology and the genetic data of 12 experimental lines. In one bacterial line, comparison between the model and the data suggests that pivotal mutations mediated by insertion sequences account for a large part of bacterial adaptation. In a more detailed analysis of one simulation, it was shown that only 0.01% of the mutations generated by a population over 10,000 generations can go to fixation as a consequence of their improved fitness. However in the model, the probability of being better fit than its parent should be set initially at ca. 10% to promote an evolution similar to the observed data.