In recent years, research data management has also become an important topic in the less data-intensive areas of the Social Sciences and Humanities (SSH). Funding agencies as well as research communities demand that empirical data collected and used for scientific research is managed and preserved in a way that research results are reproducible. In order to account for this the FAIR guiding principles for data stewardship have been established as a framework for good data management, aiming at the findability, accessibility, interoperability, and reusability of research data. This article investigates 24 European CMC corpora with regard to their compliance with the FAIR principles and discusses to what extent the deposit of research data in repositories of data preservation initiatives such as CLARIN, Zenodo or Metashare can assist in the provision of FAIR corpora.