In his 1985 paper Sullivan sketched a proof of his structural stability
theorem for differentiable group actions satisfying certain
expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and
introduce a notion of "meandering hyperbolicity" for group actions on geodesic
metric spaces. This generalization is substantial enough to encompass actions
of certain non-hyperbolic groups, such as actions of "uniform lattices" in
semisimple Lie groups on flag manifolds. At the same time, our notion is
sufficiently robust and we prove that meandering-hyperbolic actions are still
structurally stable. We also prove some basic results on meandering-hyperbolic
actions and give other examples of such actions
