This article is devoted to the control of bio-inspired robots that are underactuated. These robots are composed of tensegrity joints remotely actuated with cables, which mimic the musculoskeletal system of the bird neck. A computed torque control (CTC) is applied to these robots as well as an original control called pseudo computed torque control (PCTC). This new control uses the dynamics and the pseudo-inverse of the Jacobian matrix. The stability of the two proposed controls is then analyzed through linearization of the dynamic model and expression of the closed-loop transfer function in the Laplace domain. We show that, depending on the desired trajectory, the CTC can be unstable when the controlled variables are the end effector position and orientation. For a robot with many joints and a limited number of cables, the CTC is always unstable. Instead, the PCTC shows a large domain of stability. The analysis is complemented by experimental tests demonstrating that the CTC and PCTC exhibit similar performance when the CTC is stable. Furthermore, the PCTC maintains stability on trajectories where the CTC becomes unstable, showing robustness to perturbations as well.