  We generalize to FC*, the class of generalized FC-groups introduced in [F. de
Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes,
Serdica Math. J. 28 (2002), 241-254], a result of Baer on Engel elements. More
precisely, we prove that the sets of left Engel elements and bounded left Engel
elements of an FC*-group G coincide with the Fitting subgroup; whereas the sets
of right Engel elements and bounded right Engel elements of G are subgroups and
the former coincides with the hypercentre. We also give an example of an
FC*-group for which the set of right Engel elements contains properly the set
of bounded right Engel elements.
