  We establish a characterization of coagulation-fragmentation processes, such
that the induced birth and death processes depicting the total number of groups
at time $t\ge 0$ are time homogeneous. Based on this, we provide a
characterization of mean-field Gibbs coagulation-fragmentation models, which
extends the one derived by Hendriks et al. As a by- product of our results, the
class of solvable models is widened and a question posed by N. Berestycki and
Pitman is answered, under restriction to mean-field models.
