Because most newly arising mutations are neutral or deleterious, it has been argued(1-3) that the mutation rate has evolved to be as low as possible, limited only by the cost of error-avoidance and error-correction mechanisms, But up to one per cent of natural bacterial isolates are ’mutator’ clones that have high mutation rates(4-6). We consider here whether high mutation rates might play an important role in adaptive evolution, Models of large, asexual, clonal populations adapting to a new environment show that strong mutator genes (such as those that increase mutation rates by 1,000-fold) can accelerate adaptation, even if the mutator gene remains at a very low frequency (for example, 10(-5)), Less potent mutators (10 to 100-fold increase) can become fixed in a fraction of finite populations, The parameters of the model have been set to values typical for Escherichia coli cultures, which behave in a manner similar to the model in long-term adaptation experiments(7).