Possessive pronouns are used as determiners in English when no equivalent would be used in a Japanese sentence with the same meaning. This paper proposes a heuristic method of generating such possessive pronouns even when there is no equivalent in the Japanese. The method uses information about the use of possessive pronouns in English treated as a lexical property of nouns, in addition to contextual information about noun phrase referentiality and the subject and main verb of the sentence that the noun phrase appears in. The proposed method has been implemented in NTT Communication Science Laboratories' Japanese-to-English machine translation system ALT-J/E. In a test set of 6,200 sentences, the proposed method increased the number of noun phrases with appropriate possessive pronouns generated, by 263 to 609, at the cost of generating 83 noun phrases with inappropriate possessive pronouns.