This work seeks to explore the relationships between irony and parody, following the relevance approach to the subject, which has stressed that the expression of a certain attitude may be common to both. The work under analysis is a Spanish translation of Fowles' The French Lieutenant's Woman, which has often been described as a parody of "realist" fiction. The main aspects of this element of parody is explored, and the ways in which certain instances under study have been conveyed in a Spanish translation of this work. Resources such as parody and irony often go beyond the propositional content which is expressed in the utterances where they appear. Therefore, their translation necessarily requires strategies which transcend their "literal" level. It is felt that it is here where the proposals put forward by relevance theory may come into play, since they stress the importance of the inferential recognition of the speaker's communicative intention, which is a challenge for the translator.