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 application might be involved or impossible. A number of new 2-sliding controllers are designed by means of the proposed method based on some homogeneity reasoning. A recently developed robust exact differentiator being used as a standard part of the 2-sliding controllers, 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. Simulation results are presented.