A method and composition for the treatment of HIV and HBV infections in humans and other host animals is disclosed that includes the administration of an effective amount of a [5-carboxamido or 5-fluoro]-2′,3′-dideoxy-2′,3′-didehydro-pyrimidine nucleoside or a [5-carboxamido or 5-fluoro]-3′-modified-pyrimidine nucleoside, or a mixture or a pharmaceutically acceptable derivative thereof, including a 5′ or N4 alkylated or acylated derivative, or a pharmaceutically acceptable salt thereof, in a pharmaceutically acceptable carrier.