RNA genomes have been shown to mutate much more frequently than DNA genomes. It is generally assumed that this results in rapid evolution of RNA viral proteins. Here, an alternative hypothesis is proposed that close cooperation between positive-strand RNA viral proteins and those of the host cells required their coevolution, resulting in similar amino acid substitution rates. Constraints on compatibility with cellular proteins should determine, at any time, the covarion sets in RNA viral proteins. These ideas may be helpful in rationalizing the accumulating data on significant sequence similarities between proteins of positive-strand RNA viruses infecting evolutionarily distant hosts as well as between viral and cellular proteins.