Novel 2,4-pyrimidinedione compounds, and pharmaceutically acceptable salts thereof which possess good antiviral activities, and specifically represented by formula (I) wherein: R1 represents an unsubstituted or substituted alkyl group represented by CH¿2?CH=CR?5R6¿ or an unsubstituted or substituted propargyl group represented by CH¿2?C CR?7¿ wherein R?5, R6 and R7¿ are each independently a hydrogen atom; a methyl group optionally substituted with a halogen atom, or a C¿1-10? carbonyloxy, hydroxy, azido, cyano, optionally substituted amino, optionally substituted phosphonyl, optionally substituted phenyl, C3-10 heteroaryl, C1-3 alkoxy or benzyloxy radical; a C2-10 alkyl or alkenyl group; a cyclopropyl group; an optionally substituted phenyl group; a C3-10 heteroaryl group; a C1-10 ester group; or an optionally substituted C1-10 alkylamide group; R?2¿ represents a halogen atom, an optionally substituted C¿1-5? alkyl, C3-6 cycloalkyl, C2-8 alkenyl, C2-8 alkynyl group or a benzyl group; R?3 and R4¿ represent independently a hydrogen or halogen atom, or a hydroxy, C¿1-3? alkyl, fluoromethyl, C1-3 alkoxy, amino, C2-6 alkylester or C2-7 alkylamide group; A represents an oxygen or sulfur atom; Z represents an oxygen or sulfur atom; a carbonyl group; an amino group; or a methylene group optionally substituted with at least one selected from the group consisting of a halogen atom, and a cyano, hydroxy, azido, amino, C1-3 alkylamide, C1-4 ester, and nitro groups.