The authors extend the idea of a fourth-order model of an elastic link and introduce two complementary ways of controlling such systems. In the case of measurable joint forces/torques, they propose a control law based on a deterministic observer whose job is to recover immeasurable components of the state vector. If the forces/torques are not measurable, they propose a Kalman filter technique which uses the manipulator's model to recover the unknown states of the system. Simulation results are presented. The example used is a 6-link manipulator, UMS-2. The results encourage implementation of these control structures on a real system.>