It was previously shown that hemagglutinin residues Thr155, Glu158, and Ser228 are crucial for the recognition of Neu5Gc. In this study, we demonstrated that the ability to bind the Neu5Gc-terminated receptor is related to the amino acid 145: viruses of years 1972-1999 with Lys145 bind to the receptor, whereas viruses with Asn145 do not. Sporadic appearance and disappearance of the ability to bind Neu5Gc oligosaccharides and the absence of Neu5Gc in the composition of human glycoconjugates indicate the non-adaptive nature of this ability. It was previously shown that unlike H1N1 viruses, H3N2 viruses of years 1968-1989 did not distinguish between Neu5Acα2-6Galβ1-4Glc (6´SL) and Neu5Acα2-6Galβ1-4GlcNAc (6´SLN). H3N2 viruses isolated after 1993 have acquired the ability to distinguish between 6´SL and 6´SLN, similarly to H1N1 viruses. We found that the affinity for 6´SLN has gradually increased from 1992 to 2003. After 2003, the viruses lost the ability to bind a number of sialosides, including 6´SL, that were good receptors for earlier H3N2 viruses, and retained high affinity for 6´SLN only, which correlated with the acquisition of new glycosylation sites at positions 122, 133, and 144, as well as Glu190Asp and Gly225Asp substitutions, in hemagglutinin. These substitutions are also responsible for the receptor-binding phenotype of human H1N1 viruses. We conclude that the convergent evolution of the receptor specificity of the H1N1 and H3N2 viruses indicates that 6´SLN is the optimal natural human receptor for influenza viruses.