Marinaleda was ruled by CUT-BAI (Collective for the Unity of Workers - Andalusian Left Bloc) from 1979 until 1986, when CUT-BAI joined United Left (IU), which has since been the ruling party, although most of the members of IU's local branch are basically members of CUT-BAI.
Marinaleda's governance was controlled by CUT-BAI from 1979 to 1986, when they merged with United Left (IU).  The current ruling party is IU, and many of its local members were previously affiliated with CUT-BAI.