We prove the non-triviality of the Reeb flow for the standard contact spheres S 2n+1 , n 6 3, inside the fundamental group of their contactomorphism group. The argument uses the existence of homotopically non-trivial 2-spheres in the space of contact structures of a 3-Sasakian manifold. Let (M,ξ) be a closed contact manifold. Consider the space C(M,ξ) of contact structures isotopic to ξ. This space has been studied in special cases. See (El) for the 3-sphere and (Bo), (Ge) for torus bundles. In the present note we prove the non-triviality of its second homotopy group for 3-Sasakian manifolds, see (BG). Theorem 1. Let (M,ξ) be a 3-Sasakian manifold, then rk(π2(C(M,ξ))) ≥ 1. Let (S 4n+3 ,ξ0 = kerα0) be the standard contact sphere with the standard contact form. The non- trivial spheres in C(S 4n+3 ,ξ0) allow us to answer a question posed in (Gi):