Linked column steel frame system (LCF) is a new lateral-gravity resisting system aimed at reducing the time and costs of repairs after a seismic event. The performance objectives of this system are highly dependent on the deformations and the sequences at which fuses are formed in the structure. Therefore, in order to meet the performance objectives of this system, using a performance-based design method (e.g. the direct displacement-based design (DDBD) method), that directly controls the structural response would be useful. In the DDBD method, the equivalent viscous damping (EVD) is an important parameter which represents the energy dissipation of a structure due to its nonlinear (hysteretic) behavior. In the literature, there are some EVD expressions for conventional structural systems; however, no expression has been given for the LCF system, yet. The purpose of this study is to develop some reliable EVD expressions for the LCF systems by investigating the nonlinear behavior of 20 singlestory frame samples of different configurations with variable link beam lengths. To this end, the EVD of the frames was calculated based on their hysteretic response loops under cyclic loading. Furthermore, the EVD values was calibrated using the inelastic time-history dynamic analysis of the frames under 10 spectrum-compatible earthquake records to propose some new EVD expressions for the LCF systems with short and long link beams. The results indicate that the EVD expressions available in the literature are very conservative for the LCF systems with short link beams.