Mammalian influenza viruses are descendants of avian strains that crossed the species barrier and underwent further adaptation. Since 1997 in southeast Asia, H5N1 highly pathogenic avian influenza viruses have been causing severe, even fatal disease in humans. Although no lineages of this subtype have been established until now, such repeated events may initiate a new pandemic. As a model of species transmission, we used the highly pathogenic avian influenza virus SC35 (H7N7), which is low-pathogenic for mice, and its lethal mouse-adapted descendant SC35M. Specific mutations in SC35M polymerase considerably increase its activity in mammalian cells, correlating with high virulence in mice. Some of these mutations are prevalent in chicken and mammalian isolates, especially in the highly pathogenic H5N1 viruses from southeast Asia. These activity-enhancing mutations of the viral polymerase complex demonstrate convergent evolution in nature and, therefore, may be a prerequisite for adaptation to a new host paving the way for new pandemic viruses.