Let G = (V,E) be a simple undirected graph.A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G.This paper adresses the clique-connecting forest polytope.First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope.Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities.