A method for the antiviral treatment of an animal or patient infected with a herpes virus or a pox virus comprising administering an effective amount, of a 1,5-anhydrohexitol nucleoside analogue, or a pharmaceutical salt or ester thereof, represented by the general formula I:
- ##STR9## wherein:
- B is a heterocyclic ring which is derived from the group which consists of pyrimidine and purine bases, and
- X represents hydrogen, azido, F, Cl, Br, I, amino, --NHR.sup.2, --N(R.sup.2).sub.2, --OR.sup.2, --SR.sup.2 or CN;
- wherein R.sup.1 and R.sup.2 are the same or different, and are hydrogen, acyl, phosphate, or a branched or straight chain, saturated or unsaturated, substituted or unsubstituted hydrocarbon radical with 1-20 carbon atoms or when
- X is hydrogen, a double bond is situated between the 3- and 4- position of the 1,5-anhydro-hexitol ring, to an animal or patient for whom such therapeutic treatment is indicated and wherein said amount is effective to treat viral diseases caused by one of a herpes virus and a pox virus.