Since the 1990s written academic genres have received considerable attention in discourse and rhetorical studies, especially texts written in English. Although few studies describe PhD theses as a genre, some work has been carried out on their macrostructure and the rhetorical moves of certain sections. In the Spanish literature, genre studies on academic writing are scarce relative to those in English, especially in the case of doctoral theses. This paper analyses the introductions of 21 doctoral theses in computing written in Spanish using Bunton’s model (2002) for thesis introductions in English. The results indicate that most of the steps in this model are applicable to our corpus, but several new steps and sub-steps have been distinguished to account for the observed moves of Spanish PhD thesis introductions. The complexity of the thesis introduction is related to the scope and depth of the research carried out for a doctoral thesis, the need to display extensive knowledge of the field and to justify the relevance of the research.