The main purpose of this paper is to examine the influence of time delay associated with a semi-active variable viscous (SAVV) damper on the response of seismically excited linear and nonlinear structures. The maximum time delay is estimated on the basis of stability criteria, which consist of analyses of structural modal properties. Numerical computation of the critical time delay is performed by using dichotomic approach, which is based on multiple solving of the eigenvalue problem. Simulation results indicate that variable dampers can be effective in reducing the seismic response of structures, and that time-delay effects are important factors in control design of seismically excited structures. Furthermore, simulation results show degradation of performance whenever the actual delay exceeds the calculated critical time delay, which shows the accuracy and reliability of the proposed approach.