Universities and research centers in Spain are subject to a national open access (OA) mandate and to their own OA institutional policies, if any, but compliance with these requirements has not been fully monitored yet. We studied the degree of OA archiving of publications of 28 universities within the period 2012-2014. Of these, 12 have an institutional OA mandate, 9 do not require but request or encourage OA of scholarly outputs, and 7 do not have a formal OA statement but are well known for their support of the OA movement. The potential OA rate was calculated according to the publisher open access policies indicated in Sherpa/Romeo directory. The universities showed an asymmetric distribution of 1% to 63% of articles archived in repositories that matched those indexed by the Web of Science in the same period, of which 1% to 35% were OA and the rest were closed access. For articles on work carried out with public funding and subject to the Spanish Science law, the percentage was similar or slightly higher. However, the analysis of potential OA showed that the figure could have reached 80% in some cases. This means that the real proportion of articles in OA is far below what it could potentially be.