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The fast oscillations that occur in control systems with a second second-order sliding-mode control (2-SMC) algorithm (the so-called "suboptimal" 2-SMC algorithm) and fast actuators are investigated. It is shown that the oscillations in such control systems converge to a small vicinity of the second order sliding domain. Sufficient conditions for the existence and stability of the fast oscillations are found in terms of the properties of the corresponding Poincare maps. A demonstrative example is reported to validate the proposed results.