RNA virus replication takes place at a very high error rate, and additional increases in this parameter can produce the extinction of virus infectivity. Nevertheless, RNA viruses can adapt to conditions of increased mutagenesis, which demonstrates that selection of beneficial mutations is also possible at higher-than-standard error rates. In this study we have analysed the evolutionary behaviour of bacteriophage Qβ populations when replication proceeds in the presence of the mutagenic nucleoside analogue 5-azacytidine (AZC). We have obtained a virus population with reduced capacity to accumulate mutations in the presence of AZC and able to avoid extinction under conditions that are lethal for the wild type virus. Adapted populations fix a substitution in the readthrough protein gene and incorporate several mutations in the replicase gene that, despite having selective value, remain polymorphic after a large number of transfers in the presence of AZC.