The present invention relates to method of sustained-delivery of an active drug to a posterior part of an eye of a mammal to treat or prevent a disease or condition affecting said mammal, wherein said disease or condition can be treated or prevented by the action of said active drug upon said posterior part of the eye, comprising administering an effective amount of an ester prodrug of the active drug subconjunctivally or periocularly. Preferably, the active drug is more than about 10 times as active as the prodrug. Other aspects of this invention deal with the treatment of certain diseases by the periocular or subconjunctival delivery of an ester prodrug, and certain pharmaceutical products containing ester prodrugs for periocular or subconjunctival administration.