To obtain a new and effective medicine for treating viral diseases such as acquired immunodeficiency syndrome (AIDS), AIDS-related complication and hepatitis B, having low toxicity to hosts.

A composition for the treatment of HIV and HBV (hepatitis B virus) infections in humans and other host animals comprises 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, mixtures thereof, or a pharmaceutically acceptable derivative or derivatives thereof, including an N-1 or N-4 alkylated or acylated derivative, or a pharmaceutically acceptable salt thereof, in a pharmaceutically acceptable carrier.