Although the CSIC does not have a doctoral school nor does it have the capacity to impart university degrees, close to 4,000 doctoral theses have been defended in the last 4 years, directed by CSIC researchers.
The role of the CSIC researcher as director of the doctoral thesis is key, since he or she is ultimately responsible for the coherence and suitability of the training activities, the impact and novelty in the field of the topic of the doctoral thesis, and the guide in the planning and its adequacy, where appropriate, to that of other projects and activities where the doctoral student enrolls.
In this link you can find the list of the Universities that have an agreement with the CSIC, and in which you can request a joint doctoral thesis, as well as the different regulations that apply.
