Mechanical dampers are often installed near to anchorages of stay cables for mitigating vibrations due to wind or wind/rain. However, the optimal damping estimated by a linear theory is hard to be obtained and an efficiency factor between the designed damping and the practical one has to be considered for design. In this study, experiments of cable-damper system were conducted by using a 215 meters long full-scale stay cable. 7 types of mechanical dampers, including oil damper, viscous damper and MR damper, were adopted. The experimental results show that an inner type damper provided an additional damping (log decrement) 0.013, other outer type dampers provided additional damping larger than 0.030. Based on the experimental results, the authors suggest that the efficiency factor should be 0.3 for an inner type damper, and 0.5 for an outer type damper. The nonlinear design theory was also preliminarily studied.