This paper presents the research project the PACTE group is carrying out on 'Establishing Competence Levels in the Acquisition of Translation Competence in Written Translation'. A continuation of PACTE's previous experimental research on translation competence and its acquisition, the project aims to propose level descriptors as a first step towards developing a common European framework of reference for translation's academic and professional arenas, both of which are represented among its participants. The project is organized into three stages, the first of which involved the production of a first level descriptor proposal, including a three-level scale with sub-levels and five descriptive categories (language competence; cultural, world knowledge and thematic competence; instrumental competence; translation service provision competence; and translation problem solving competence). In the second stage, the proposal produced is to be evaluated by experts from the academic and professional arenas. In the third stage, the data obtained through the expert judgement process will be analysed and the proposal revised. This paper sets out the project's objectives, our grounds for undertaking it, its conceptual framework and its methodology, as well as the results obtained in the first stage and the future direction of the research. [This article was co-authored by PACTE Group.]