Imidazole compounds having adenosine deaminase inhibitory activity represented by formula (I) wherein R1 is hydrogen, hydroxy, protected hydroxy, or aryl optionally substituted with suitable substituent(s); R2 is hydrogen or lower alkyl; R3 is hydroxy or protected hydroxy; R4 is cyano, (hydroxy)iminoamino(lower)alkyl, carboxy, protected carboxy, heterocyclic group optionally substituted with amino, or carbamoyl optionally substituted with suitable substituent(s); and -A- is -Q- or -O-Q-, wherein Q is single bond or lower alkylene, provided that when R2 is lower alkyl, then R1 is hydroxy, protected hydroxy, or aryl optionally substituted with suitable substituent(s), its prodrug, or their salt. The compounds are useful for treating and/or preventing diseases for which adenosine is effective.