Abstract: With the continuous increase in the length of stay cables in cable-stayed bridges, a damper installed at a point near the cable-deck end is inadequate for cable vibration control. Meanwhile, previous studies have shown that cable sag effect weakens the damping effect of the damper. Therefore, it studies free vibrations of long cables with viscous dampers installed respectively on two points of a cable (cable-two-damper system) and performs complex modal analysis of the system with the sag effect taken into consideration. Asymptotic formulas for modal damping estimation has been derived considering the fact that each damper is close to one cable end in practice. Parametric studies on damper coefficients and locations are carried out to maximize cable damping. The results show that when a cable is equipped with two dampers, cable sag still has an negative effect on cable modal damping in nearly symmetric modes, but has no effect in nearly antisymmetric modes; When the two dampers are symmetrically installed on a cable near its ends, the total modal damping of the cable is approximately the sum of the contributions from each damper when installed separately. It is also found that the dampers both installed at the same cable end cannot improve the maximal attainable damping for a single mode, which can be achieved by only installing one damper farther from the cable end; however, they can achieve better multimode damping effects in terms of simultaneously suppressing high and low mode vibrations of the cable.