Collaborative robots (or cobots) are robots that can safely operate together or interact with humans in a shared environment. They have steadily been more prevalent in recent years. The use of compliant actuators is critical in the design of cobots. In fact, this form of actuation system can potentially mitigate the damage caused by unexpected collision. As a result, when working in a complex setting, elastic joints are thought to outperform rigid joints. In this paper, a two-loop adaptive controller is proposed to deal with the control task of a 2-DOF robot arm with elastic actuators. For the outer control loop, an adaptive sliding mode controller (ASMC) is proposed to deal with uncertainties and disturbance on the load side of the robot arm. For the inner loop, model reference adaptive controllers (MRAC) are proposed to handle the uncertainties on the load side of the robot arm. Simulation experiments are conducted to verify the efficiency of the proposed two-loop controller.