Let f : M → R be a Morse-Bott function on a closed manifold M , so the set Σ f of its critical points is a closed submanifold whose connected components may have distinct dimensions. Denote by S(f ) = {h ∈ D(M ) | f • h = f } the group of diffeomorphisms of M preserving f and let D(Σ f ) be the group of diffeomorphisms of Σ f . We prove that the "restriction to Σ f " map ρ : S(f ) → D(Σ f ), ρ(h) = h| Σ f , is a locally trivial fibration over its image ρ(S(f )).2010 Mathematics Subject Classification. 57R30, 57R45, 53B15,