The FG nucleoporins (FG Nups) function at the nuclear pore complex (NPC) to facilitate nucleocytoplasmic transport. In Saccharomyces cerevisiae, each FG Nup contains a large natively unfolded domain that is punctuated by phenylalanine-glycine (FG) repeats. These FG repeats are surrounded by hydrophilic amino acids (AAs) common to disordered protein domains. Here we show that the FG domain of Nups from human, fly, worm and other yeast species are also enriched in these disorder-associated AAs, indicating that structural disorder is a conserved feature of FG Nups and likely serves an important role in NPC function. Despite the conservation of AA composition, FG Nup sequences from different species show extensive divergence. A comparison of the AA substitution rates of proteins with syntenic orthologs in four Saccharomyces species reveals that FG Nups have evolved at twice the rate of average yeast proteins, with most substitutions occurring in sequences between FG repeats. The rapid evolution of FG Nups is poorly explained by parameters known to influence AA substitution rate, such as protein expression level, interactivity and essentiality; instead, their rapid evolution may reflect an intrinsic permissiveness of natively unfolded structures to AA substitutions. The overall lack of AA sequence conservation in FG Nups is sharply contrasted by discrete stretches of conserved sequences. These conserved sequences highlight known karyopherin and nucleoporin binding sites as well as other uncharacterized sites that may have important structural and functional properties.