Interferon-alpha (IFN.alpha.) analog proteins modified by chemical attachment of at least one hydrophilic polymer moiety, such as polyethylene glycol chain, are described. In one embodiment, the IFN.alpha. analog protein has an amino acid sequence that differs from a native human IFN.alpha. interferon-alpha by one or more amino acid residues in the N-terminal region, comprised of between about residues 1-27, inclusive, by one or more substitutions selected based on the amino acid residue at the corresponding position of a mature interferon-tau (IFN.tau.) protein. Methods of treating viral diseases and other disorders with the polymer-modified IFN.alpha. analog protein are also described.