Abstract. We consider generalized Galileon theories within general relativity in four-dimensional space-time. We provide the argument showing that the generalized Galileons described by a wide class of Lagrangians do not admit stable, static, spherically symmetric semi-closed worlds. We also show that in a class of theories with ⊥ = − (where ⊥ is transverse pressure and is energy density), semi-closed worlds, if exist, would be observed as objects of negative mass.