N-substituted 5-hydroxypyrimidin-6-one-4-carboxamides of formula (I): are described as inhibitors of HIV integrase and inhibitors of HIV replication, wherein R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are defined herein. These compounds are useful in the prevention and treatment of infection by HIV and in the prevention, delay in the onset, and treatment of AIDS. The compounds are employed against HIV infection and AIDS as compounds per se or in the form of pharmaceutically acceptable salts. The compounds and their salts can be employed as ingredients in pharmaceutical compositions, optionally in combination with other antivirals, immunomodulators, antibiotics or vaccines. Methods of preventing, treating or delaying the onset of AIDS and methods of preventing or treating infection by HIV are also described ##STR00001##