BACKGROUND: The interpandemic evolution of the influenza A virus hemagglutinin (HA) protein is commonly considered a paragon of rapid evolutionary change under positive selection in which amino acid replacements are fixed by virtue of their effect on antigenicity, enabling the virus to evade immune surveillance. RESULTS: We performed phylogenetic analyses of the recently obtained large and relatively unbiased samples of the HA sequences from 1995-2005 isolates of the H3N2 and H1N1 subtypes of influenza A virus. Unexpectedly, it was found that the evolution of H3N2 HA includes long intervals of generally neutral sequence evolution without apparent substantial antigenic change (stasis periods) that are characterized by an excess of synonymous over nonsynonymous substitutions per site, lack of association of amino acid replacements with epitope regions, and slow extinction of coexisting virus lineages. These long periods of stasis are punctuated by shorter intervals of rapid evolution under positive selection during which new dominant lineages quickly displace previously coexisting ones. The preponderance of positive selection during intervals of rapid evolution is supported by the dramatic excess of amino acid replacements in the epitope regions of HA compared to replacements in the rest of the HA molecule. In contrast, the stasis intervals showed a much more uniform distribution of replacements over the HA molecule, with a statistically significant difference in the rate of synonymous over nonsynonymous substitution in the epitope regions between the two modes of evolution. A number of parallel amino acid replacements - the same amino acid substitution occurring independently in different lineages - were also detected in H3N2 HA. These parallel mutations were, largely, associated with periods of rapid fitness change, indicating that there are major limitations on evolutionary pathways during antigenic change. The finding that stasis is the prevailing modality of H3N2 evolution suggests that antigenic changes that lead to an increase in fitness typically result from epistatic interactions between several amino acid substitutions in the HA and, perhaps, other viral proteins. The strains that become dominant due to increased fitness emerge from low frequency strains thanks to the last amino acid replacement that completes the set of replacements required to produce a significant antigenic change; no subset of substitutions results in a biologically significant antigenic change and corresponding fitness increase. In contrast to H3N2, no clear intervals of evolution under positive selection were detected for the H1N1 HA during the same time span. Thus, the ascendancy of H1N1 in some seasons is, most likely, caused by the drop in the relative fitness of the previously prevailing H3N2 lineages as the fraction of susceptible hosts decreases during the stasis intervals. CONCLUSIONS: We show that the common view of the evolution of influenza virus as a rapid, positive selection-driven process is, at best, incomplete. Rather, the interpandemic evolution of influenza appears to consist of extended intervals of stasis, which are characterized by neutral sequence evolution, punctuated by shorter intervals of rapid fitness increase when evolutionary change is driven by positive selection. These observations have implications for influenza surveillance and vaccine formulation; in particular, the possibility exists that parallel amino acid replacements could serve as a predictor of new dominant strains.