The theory of Fitting classes is, by now, a well established part of the theory of finite soluble groups. In contrast, Fitting classes have received rather scant attention in infinite groups, although some recent work of Beidleman and Karbe  and Beidleman, Karbe and Tomkinson  suggest that one can obtain results in this direction. The paper , cited above, in fact generalizes earlier work of Tomkinson  to the class of locally soluble FC-groups. The present paper is concerned with the theory of Fitting classes in a class of groups somewhat similar to the class of FC-groups, namely the class of CC-groups, introduced by Polovickiǐ in . A group G is a CC-group if G/CG(xG) is a Černikov group for all x ∈ G where, as in the rest of this paper, we use the standard group theoretic notation of . Recently, Alcázar and Otal  have shown how to generalize results of B. H. Neumann  to the class of CC-groups. The main purpose of the present note is to illustrate further how one can handle CC-groups, in an analogous manner to FC-groups, by using techniques similar to those used in  and .