Cirici would like to acknowledge financial support from the German Research Foundation (SPP-1786) and partial support from the Spanish Ministry of Economy and Competitiveness (MTM2016-76453-C2-2-P). Roig is partially supported by projects MTM2012-38122-C03-01/FEDER and 2014 SGR 634.

We prove the existence of Sullivan minimal models of operad algebras for a quite wide family of operads in the category of complexes of vector spacesover a field of characteristic zero. Our construction is an adaptation of Sullivan's original step by step construction to the setting of operad algebras. The family of operads that we consider includes all operads concentrated in degree 0 as well as their minimal models. In particular, this gives Sullivan minimal models for algebras over Com, Ass, and Lie, as well as over their minimal models Com∞, Ass∞, and Lie∞. Other interesting operads, such as the operad Ger encoding Gerstenhaber algebras, also fit in our study.