We give an exposition of results of Baldwin–Shelah [2] on saturatedfree algebras, at the level of generality of complete first order theoriesT with a saturated model M which is in thealgebraic closure of an indiscernible set. We then make some new observationswhen M is a saturated free algebra, analogous to (moredifficult) results for the free group, such as a description of forking.