This work analyses the translation of wordplay in the parallel corpus of Tom Stoppard’s play Travesties and its translation into Croatian. The translation of wordplay is analysed according to Dirk Delabastita’s classification of translation strategies for wordplay translation. The main goal of the study is to determine whether wordplay is retained in the target text or whether it is omitted. This is determined based on the qualitative analysis of wordplay according to Dealabastita’s strategies and on the quantitative analysis of each translation strategy in order to determine which strategy was most often used. Also, all identified instances of wordplay are determined according to the type of wordplay based on its main principle of formation. Since Travesties is a play containing numerous examples of intertextuality and citations of other literary works, the most prominent of them being James Joyce’s Ulysses, this work also analyses the translation of Joyce’s wordplay incorporated into Travesties and compares it to the previously published translation of Ulysses into Croatian. The results show that both tendencies of retaining and omitting wordplay in the target text are present, but that wordplay is most often translated by wordplay. The translation of Joyce’s wordplay is, however, not based on the previous translation of Ulysses.