Two output feedback controllers based on the Continuous Twisting Algorithm are provided. In those controllers, the state observers are based on the first and the second order Robust Exact Differentiators. The stability of the closed loops is proven through input-to-state stability properties. In the case of the second order differentiator, the conservation of homogeneity allows the output feedback scheme to preserve the robustness and accuracy properties of the state feedback Continuous Twisting Algorithm. In the same case, a smooth homogeneous Lyapunov function is constructed for the closed loop. A separation principle in the design of the controller and the observers is established. A qualitative analysis of the performance of the controllers in the presence of noise in the measurement is carried out. One of the schemes is used for output feedback control of a class of nonlinear systems. (C) 2018 Elsevier Ltd. All rights reserved.