This is a joint work with G. Courtois, S. Gallot and A. Sambusetti. We shall prove that, given two positive numbers and H, there are finitely non cyclic torsion-free -hyperbolic marked groups (Γ.Σ) satisfying Ent(Γ,Σ)≤H, up to isometry (of marked groups). Here a marked group is a group Γ together with a symmetric generating set and Ent is the entropy of the marked group. The talk is intended to be elementary; the purpose is to define all these notions and give a flavour of the proof.