Second-order sliding modes are used to keep exactly a constraint of the second relative degree or just to avoid chattering, i.e. in the cases when the standard (first order) sliding mode implementation might be involved or impossible. Design of a number of new 2-sliding controllers is demonstrated by means of the proposed homogeneity-based approach. A recently developed robust exact differentiator being applied, robust output-feedback controllers with finite-time convergence are produced, capable to control any general uncertain single-input-single-output process with relative degree 2. An effective simple procedure is developed to attenuate the I-sliding mode chattering. Simulation of new controllers is presented. (C) 2007 Elsevier Ltd. All rights reserved.