The living world exists in the present form because of the evolutionary processes that have been going on since the origin of life on earth. Mutations that are random changes in the genetic material of a cell or an organism are one of the main drivers of the evolutionary processes. My aim is to obtain a very detailed understanding of the evolution of mutation rates in an adapted asexual population, on which the theoretical works have been very few. In my model, I study the chances of ﬁxation of an individual with a lower mutation rate (nonmutator) in a population evolving on a single-peaked ﬁtness landscape in which the strength of the interactions among mutations (epistasis) can be tuned. I use the Wright-Fisher process to deal with ﬁnite populations and the multitype branching process to understand the chances of ﬁxation of a nonmutator in a large population. The results I obtained will be discussed in detail in the talk.