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An interpretation to the physics of stable geodesics of massive particles in black hole backgrounds has been recently proposed in the context of the AdS/CFT correspondence. It was argued that the existence of stable orbits indicates that the dual state does not thermalize on a thermal time scale and the bulk excitations can be interpreted as metastable states in the dual field theory. Here we study motion of massive particles in the background of the D-dimensional asymptotically anti-de Sitter (AdS) black holes in the Einstein-Lovelock theory. We show that, unlike the asymptotically flat case, for any kind of higher curvature Lovelock corrections there appear a stable circular orbit at a distance from the black hole. We find the general analytical expressions for the frequencies of distant circular orbits and radial oscillation frequencies. We show that the corresponding correction has the same power as in the Schwarzschild-AdS case, implying a universal scaling with the temperature for any Lovelock theory.