A Lithuanian sentence with a dative and an accusative object can be translated into English in five different ways: using the English “internal dative” construction, the constructions with the prepositions to, for, on, and a possessive modifier. The question whether the Lithuanian sentences with dative and accusative objects are instances of the same construction or whether they are only superficially similar instances of different underlying structures is addressed in the paper. Dąbrowska (1997) dealing with similar constructions in Polish introduced the concept of the Target Person supplemented by the notion of the personal sphere as the central concept in the interpretation and understanding of the construction with dative and accusative objects. The concept of the Target Person supplemented with the notion of personal sphere is very closely related to the concept of Possession used in linguistics (cf. Seliverstova 1990, Grigaliūnienė 1989, Heine 1997). An attempt is made to look at the sentences under consideration as possessive. The Lithuanian dative is only used when the referent of the first indirect object is affected by the action performed, when it becomes the possessor of the result of the action performed upon the patient.